AMENDMENT ANDEXCHANGE AGREEMENT

Exhibit 10.1

EXECUTION COPY

AMENDMENT AND EXCHANGE AGREEMENT

This Amendment and Exchange Agreement (the “Agreement”) is entered into as of the 2nd day of April, 2015, by and among Amedica Corporation, a Delaware corporation with offices located at 1885 West 2100 South, Salt Lake City, UT 84119 (the “Company”), and MG Partners II, Ltd. (the “Holder”), with reference to the following facts:

A. In accordance with that certain Securities Purchase Agreement, dated as of June 30, 2014, by and among the Company and the Holder (the “Securities Purchase Agreement”), the Company issued to the Holder (i) $6,400,000 in aggregate principal amount of senior convertible notes (the “Existing Notes”, as converted the “Existing Conversion Shares”), (ii) shares of the Company’s common stock, $0.01 par value per share (the “Common Stock”) and (iii) a warrant to purchase shares of Common Stock (the “Existing Warrant”);

B. The Company has duly authorized the issuance to the Holder of a new senior convertible note in the form attached hereto as Exhibit A in exchange for the Existing Notes and the Existing Warrant (the “Exchange Notes”, as exercised, the “Exchanged Conversion Shares, and together with the Exchange Notes, collectively, the “Exchange Securities”);

C. Each of the Company and the Holder desire to effectuate such exchange on the basis and subject to the terms and conditions set forth in this Agreement;

D. The exchange of the Existing Notes and the Existing Warrant for the Exchange Notes is being made in reliance upon the exemption from registration provided by Section 3(a)(9) of the Securities Act of 1933, as amended (the “Securities Act”);

E. Capitalized terms used but not otherwise defined herein shall have the meanings as set forth in the Securities Purchase Agreement (as amended hereby).

NOW, THEREFORE, in consideration of the foregoing premises and the mutual covenants hereinafter contained, the parties hereto agree as follows:

1. Exchange of Securities. On the Effective Date (as defined below), pursuant to Section 3(a)(9) of the Securities Act, the Holder hereby agrees to convey, assign and transfer the Existing Notes and the Existing Warrant to the Company in exchange for which the Company agrees to issue the Exchange Notes to the Holder as follows (such transactions in this Section 1, the “Exchange”).

(a) In exchange for the Existing Notes and the Existing Warrant, on the date hereof the Company shall deliver or cause to be delivered to the Holder (or its designee) the Exchange Notes at the address for delivery set forth on the signature page of the Holder. For the avoidance of doubt, the principal amount and other amounts outstanding under each of the Exchange Notes shall be the identical principal amount and other amounts then outstanding under the corresponding Existing Notes.

(b) The Holder shall deliver or cause to be delivered to the Company (or its designee) the Existing Notes and the Existing Warrant as soon as commercially practicable following the date hereof. Immediately following the delivery of the Exchange Notes to the Holder (or its designee) (such time, the “Delivery Time”), the Existing Notes and the Existing Warrant shall be cancelled.

(c) The Company and the Holder shall execute and/or deliver such other documents and agreements as are customary and reasonably necessary to effectuate the Exchange.

2. AMENDMENTS TO TRANSACTION DOCUMENTS.

(a) Ratifications. Except as otherwise expressly provided herein, the Securities Purchase Agreement and each other Transaction Document, is, and shall continue to be, in full force and effect and is hereby ratified and confirmed in all respects, except that on and after the Delivery Time: (i) all references in the Securities Purchase Agreement to “this Agreement”, “hereto”, “hereof”, “hereunder” or words of like import referring to the Securities Purchase Agreement shall mean the Securities Purchase Agreement as amended by this Agreement, (ii) all references in the other Transaction Documents, to the “Securities Purchase Agreement”, “thereto”, “thereof”, “thereunder” or words of like import referring to the Securities Purchase Agreement shall mean the Securities Purchase Agreement as amended by this Agreement, (iii) all references in the Registration Rights Agreement to “this Agreement”, “hereto”, “hereof”, “hereunder” or words of like import referring to the Registration Rights Agreement shall mean the Registration Rights Agreement as amended by this Agreement, and (iv) all references in the other Transaction Documents to the “Registration Rights Agreement”, “thereto”, “thereof”, “thereunder” or words of like import referring to the Registration Rights Agreement shall mean the Registration Rights Agreement as amended by this Agreement.

(b) Amendments to Transaction Documents. On and after the Closing Date, each of the Transaction Documents are hereby amended as follows:

(i) The defined term “Notes” is hereby amended to include the “Exchange Notes (as defined in the Amendment and Exchange Agreement)”.

(ii) The defined term “Conversion Shares” is hereby amended to include the “Exchanged Conversion Shares (as defined in the Amendment and Exchange Agreement)”.

(iii) The defined term “Amendment and Exchange Agreement” shall mean “that certain Amendment and Exchange Agreement, dated as of April 2, 2015, by and between the Company and the Investor”.

(iv) The defined term “Transaction Documents” is hereby amended to include the Amendment and Exchange Agreement.

(v) Section 4.6 of the Securities Purchase Agreement is hereby amended to replace “below $2.50” with “below $0.50” (as adjusted for stock splits, stock dividends, recapitalizations and similar events)”.

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3. Representations and Warranties of the Company. The Company represents and warrants to the Holder, as of the date hereof, and as of the time of consummation of the Exchange, that:

(a) Organization and Qualification. The Company and each Subsidiary are duly incorporated or otherwise organized, validly existing and in good standing under the laws of the jurisdiction of its incorporation or organization (as applicable), with the requisite power and authority to own and use its properties and assets and to carry on its business as currently conducted. Neither the Company nor any Subsidiary is in violation of any of the provisions of its respective certificate or articles of incorporation, bylaws or other organizational or charter documents except, with respect to the Subsidiaries, for violations which would not, individually or in the aggregate, have or reasonably be expected to result in a Material Adverse Effect. The Company and each Subsidiary are duly qualified to conduct its respective businesses and are in good standing as a foreign corporation or other entity in each jurisdiction in which the nature of the business conducted or property owned by it makes such qualification necessary, except where the failure to be so qualified or in good standing, as the case may be, would not, individually or in the aggregate, have or reasonably be expected to result in a Material Adverse Effect.

(b) Authorization and Binding Obligation. The Company has the requisite power and authority to enter into and perform its obligations under this Agreement and each of the other agreements and certificates entered into by the parties hereto in connection with the transactions contemplated by this Agreement (collectively, the “Exchange Documents”) and to issue the Exchange Securities in accordance with the terms hereof and thereof. The execution and delivery of the Exchange Documents by the Company and the consummation by the Company of the transactions contemplated hereby and thereby, including, without limitation, the issuance of the Exchange Securities, have been duly authorized by the Board of Directors of the Company and, other than (i) such filings required under applicable securities or “Blue Sky” laws of the states of the United States, (ii) no further filing, consent, or authorization is required by the Company or of its Board of Directors or its shareholders. This Agreement and the other Exchange Documents have been duly executed and delivered by the Company and constitute the legal, valid and binding obligations of the Company enforceable against the Company in accordance with their respective terms, except as such enforceability may be limited by general principles of equity or applicable bankruptcy, insolvency, reorganization, moratorium, liquidation or similar laws relating to, or affecting generally, the enforcement of applicable creditors’ rights and remedies.

(c) No Conflict; Required Filings and Consents.

(i) The execution, delivery and performance of the Exchange Documents by the Company and the consummation by the Company of the transactions contemplated hereby and thereby (including, without limitation, the issuance of the Exchange Notes and reservation for issuance and issuance of the Exchanged Conversion Shares) will not (A) result in a violation of the Certificate of Incorporation, the terms of any share capital of the Company or any of its Subsidiaries, the Bylaws or any of the organizational documents of the Company or any of its Subsidiaries or (B) conflict with, or constitute a default (or an event which with notice or lapse of time or both would become a default) under, or give

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to others any rights of termination, amendment, acceleration or cancellation of, any agreement, indenture or instrument to which the Company or any of its Subsidiaries is a party, or (C) result in a violation of any law, rule, regulation, order, judgment or decree (including U.S. federal and state securities laws, rules, and regulations, and the rules and regulations of the Nasdaq Capital Market (the “Principal Market”) applicable to the Company or any of its Subsidiaries or by which any property or asset of the Company or any of its Subsidiaries is bound or affected.

(ii) Neither the Company nor any of its Subsidiaries is required to obtain any consent, authorization or order of, or, make any filing or registration with, any court, governmental agency or any regulatory or self-regulatory agency or any other Person in order for it to execute, deliver or perform any of its obligations under or contemplated by the Exchange Documents, in each case in accordance with the terms hereof or thereof. All consents, authorizations, orders, filings and registrations (which the Company is required to obtain pursuant to the preceding sentence) have been obtained or effected, or will have been obtained or effected, on or prior to the date hereof, and the Company and its Subsidiaries are unaware of any facts or circumstances that might prevent the Company from obtaining or effecting any of the registration, application or filings pursuant to the preceding sentence. With the exception of the February 19, 2015 letter from the NASDAQ OMX GROUP notifying the Company that the bid price of the Company’s common stock for the last 30 consecutive trading days had closed below the minimum $1.00 per share required for continued listing under Listing Rule 5550(a)(2), the Company is not in violation of the listing requirements of the Principal Market and has no knowledge of any other facts that would reasonably lead to delisting or suspension of the shares of Common Stock by the Principal Market in the foreseeable future.

(d) No Integration. None of the Company, its Subsidiaries, any of their affiliates, or any Person acting on their behalf has, directly or indirectly, made any offers or sales of any security or solicited any offers to buy any security, under circumstances that would require registration of any of Exchange Securities under the Securities Act or cause this offering of the Exchange Securities to be integrated with prior offerings by the Company for purposes of the Securities Act or any applicable shareholder approval provisions, including, without limitation, under the rules and regulations of any exchange or automated quotation system on which any of the securities of the Company are listed or designated. None of the Company, its Subsidiaries, their affiliates or any Person acting on their behalf will take any action or steps referred to in the preceding sentence that would require registration of any of Exchange Securities under the Securities Act or cause the offering of the Exchange Securities to be integrated with other offerings.

(e) Securities Law Exemptions. Assuming the accuracy of the representations and warranties of the Holder contained herein, the offer and issuance by the Company of the Exchange Securities is exempt from registration under the Securities Act and all applicable state securities laws. The offer and issuance of the Exchange Securities is exempt from registration under the Securities Act pursuant to the exemption provided by Section 3(a)(9) thereof.

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(f) Issuance of Exchange Securities. The issuance of the Exchange Notes is duly authorized and upon issuance in accordance with the terms of the Exchange Documents shall be validly issued, fully paid and non-assessable and free from all taxes, liens, charges and other encumbrances with respect to the issue thereof. Upon issuance in accordance with the Exchange Notes, the Exchanged Conversion Shares will be validly issued, fully paid and nonassessable and free from all preemptive or similar rights, taxes, liens, charges and other encumbrances with respect to the issue thereof, with the holders being entitled to all rights accorded to a holder of Common Stock.

(g) No Consideration Paid. No commission or other remuneration has been paid by Company for soliciting the exchange of the Existing Warrant for the Exchange Securities as contemplated hereby.

(h) Disclosure. Other than as set forth in the Press Release (as defined below), the Company confirms that neither it nor any other Person acting on its behalf has provided the Holder or its agents or counsel with any information that constitutes or could reasonably be expected to constitute material, nonpublic information. The Company understands and confirms that the Holder will rely on the foregoing representations in effecting transactions in the Exchange Securities. All disclosure provided to the Holder regarding the Company and its Subsidiaries, their business and the transactions contemplated hereby, including the schedules to this Agreement, furnished by or on behalf of the Company is true and correct and does not contain any untrue statement of a material fact or omit to state any material fact necessary in order to make the statements made therein, in the light of the circumstances under which they were made, not misleading. No event or circumstance has occurred or information exists with respect to the Company or any of its Subsidiaries or its or their business, properties, prospects, operations or financial conditions, which, under applicable law, rule or regulation, requires public disclosure or announcement by the Company but which has not been so publicly announced or disclosed.

4. Representations and Warranties of Holders. The Holder represents and warrants to the Company , as of the date hereof, as follows:

(a) Organization and Authority. The Holder has the requisite power and authority to enter into and perform its obligations under this Agreement. The execution and delivery of this Agreement by the Holder and the consummation by Holder of the transactions contemplated hereby has been duly authorized by Holder’s board of directors or other governing body. This Agreement has been duly executed and delivered by Holder and constitutes the legal, valid and binding obligation of Holder, enforceable against Holder in accordance with its terms.

(b) Ownership of Warrants. The Holder owns the Existing Notes and the Existing Warrant free and clear of any liens (other than the obligations pursuant to this Agreement, the Transaction Documents and applicable securities laws).

(c) Reliance on Exemptions. The Holder understands that the Exchange Securities are being offered and exchanged in reliance on specific exemptions from the registration requirements of United States federal and state securities laws and that the Company is relying in part upon the truth and accuracy of, and the Holder’s compliance with, the representations, warranties, agreements, acknowledgments and understandings of the Holder set forth herein and in the Exchange Documents in order to determine the availability of such exemptions and the eligibility of the Holder to acquire the Exchange Securities.

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(d) Validity; Enforcement. This Agreement and the Exchange Documents to which the Holder is a party have been duly and validly authorized, executed and delivered on behalf of the Holder and shall constitute the legal, valid and binding obligations of the Holder enforceable against the Holder in accordance with their respective terms, except as such enforceability may be limited by general principles of equity or to applicable bankruptcy, insolvency, reorganization, moratorium, liquidation and other similar laws relating to, or affecting generally, the enforcement of applicable creditors’ rights and remedies.

(e) No Conflicts. The execution, delivery and performance by the Holder of this Agreement and the Exchange Documents to which the Holder is a party, and the consummation by the Holder of the transactions contemplated hereby and thereby will not (i) result in a violation of the organizational documents of the Holder or (ii) conflict with, or constitute a default (or an event which with notice or lapse of time or both would become a default) under, or give to others any rights of termination, amendment, acceleration or cancellation of, any agreement, indenture or instrument to which the Holder is a party, or (iii) result in a violation of any law, rule, regulation, order, judgment or decree (including federal and state securities laws) applicable to the Holder, except in the case of clauses (ii) and (iii) above, for such conflicts, defaults, rights or violations which would not, individually or in the aggregate, reasonably be expected to have a material adverse effect on the ability of the Holder to perform its obligations hereunder.

(f) No Consideration Paid. No commission or other remuneration has been paid by the Holder for soliciting the exchange of the Existing Notes and the Existing Warrant for the Exchange Notes as contemplated hereby.

5. Mutual Release. Effective as of the Delivery Time, each party hereto on behalf of itself and its affiliates (collectively, the “Releasing Parties”) hereby unconditionally release and forever discharge the other party hereto, including, but not limited to, all of such other party’s present and former subsidiaries, affiliate companies, shareholders, officers, directors, employees, attorneys and agents (collectively, the “Released Parties”), from any and all causes of action demands claims contracts, encumbrances, liabilities, obligations, expenses, losses, and rights of every nature and description, whether arising or pleaded in law or in equity, under contract, statute, tort or otherwise, whether known or unknown, whether accrued, potential, inchoate, liquidated, contingent or actual, asserted or that might have been asserted (“Claims”) which the Releasing Parties now have, have ever had or may hereafter have, accruing or arising contemporaneously with, or before the date hereof, including all Claims based upon, arising out of, or in any way relating to, the Securities Purchase Agreement, the Existing Note, the Existing Warrant or any other Transaction Document, other than Claims arising pursuant to this Agreement, the Exchange Notes or any other Exchange Document. For the avoidance of doubt, this mutual release shall not release any Releasing Party of its obligations, if any, under this Agreement, the Exchange Notes or any other Exchange Document.

6. Disclosure of Transaction. The Company shall, on or before 8:30 a.m., New York City Time, on the first business day after the date of this Agreement, issue a press release and/or Current Report on Form 8-K (collectively, the “Press Release”) disclosing all material terms of the transactions contemplated hereby. From and after the issuance of the Press Release,

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the Holder shall not be in possession of any material, nonpublic information received from the Company or any of its respective officers, directors, employees or agents, that is not disclosed in the Press Release. The Company shall not, and shall cause its officers, directors, employees and agents, not to, provide the Holder with any material, nonpublic information regarding the Company from and after the filing of the Press Release without the express written consent of the Holder. The Company shall not disclose the name of the Holder in any filing, announcement, release or otherwise, unless such disclosure is required by law or regulation.

7. No Integration. None of the Company, its Subsidiaries, any of their affiliates, or any Person acting on their behalf shall, directly or indirectly, make any offers or sales of any security (as defined in the Securities Act) or solicit any offers to buy any security or take any other actions, under circumstances that would require registration of any of the Exchange Securities under the Securities Act or cause this offering of the Exchange Securities to be integrated with such offering or any prior offerings by the Company for purposes of the Securities Act or any applicable shareholder approval provisions, including, without limitation, under the rules and regulations of the Principal Market and/or any exchange or automated quotation system on which any of the securities of the Company are listed or designated.

8. Listing. The Company shall promptly secure the listing or designation for quotation (as applicable) of all of the Exchanged Conversion Shares upon each national securities exchange and automated quotation system, if any, upon which the Common Stock is then listed or designated for quotation (as applicable) (subject to official notice of issuance) and shall maintain such listing of all the Exchanged Conversion Shares from time to time issuable under the terms of the Exchange Documents. The Company shall maintain the Common Stock’s authorization for quotation on the Principal Market. Neither the Company nor any of its Subsidiaries shall take any action which would be reasonably expected to result in the delisting or suspension of the Common Stock on the Principal Market. The Company shall pay all fees and expenses in connection with satisfying its obligations under this Section 7.

9. Fees. The Company shall reimburse Kelley Dyre & Warren LLP (counsel to the Holder), on demand, for all reasonable, documented costs and expenses incurred by it in connection with preparing and delivering this Agreement (including, without limitation, all reasonable, documented legal fees and disbursements in connection therewith, and due diligence in connection with the transactions contemplated thereby) in an aggregate amount not to exceed $25,000.

10. Holding Period. For the purposes of Rule 144, the Company acknowledges that the holding period of (i) the Exchange Notes (and upon conversion of the Exchange Notes, the Exchanged Conversion Shares) may be tacked onto the holding period of the Existing Notes and the Existing Warrants and, and the Company agrees not to take a position contrary to this Section 9. The Company agrees to take all actions, including, without limitation, the issuance by its legal counsel of any necessary legal opinions, necessary to issue the Exchange Conversion Shares that are freely tradable on the Principal Market without restriction and not containing any restrictive legend without the need for any action by the Holder.

11. Stockholder Approval. The Company shall provide each stockholder entitled to vote at a special or annual meeting of stockholders of the Company (the “Stockholder Meeting”), which shall be promptly called and held not later than May 31, 2015 (the “Stockholder Meeting Deadline”), a proxy statement, substantially in a form which shall have

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been previously reviewed by Kelley Drye & Warren LLP, at the expense of the Company but in any event such expense not to exceed $5,000 without the prior written approval of the Company; soliciting each such stockholder’s affirmative vote at the Stockholder Meeting for approval of approval of resolutions (“Stockholder Resolutions”) providing for the issuance of all of the Securities (including the Exchange Securities) as described in the Transaction Documents (as amended hereby) in accordance with applicable law and the rules and regulations of the Principal Market (such affirmative approval with respect to the Stockholder Resolutions, the “Stockholder Approval”, and the date the Stockholder Approval is obtained, the “Stockholder Approval Date”), and the Company shall use its reasonable best efforts to solicit its stockholders’ approval of such resolutions and to cause the Board of Directors of the Company to recommend, to the extent possible consistent with its fiduciary duties under Delaware law, to the stockholders that they approve the Stockholder Resolutions. The Company shall retain a nationally recognized proxy solicitor to assist in obtaining approval of the stockholders of the Company to the Resolution. The Company shall be obligated to seek to obtain the Stockholder Approval by the Stockholder Meeting Deadline. If, despite the Company’s reasonable best efforts the Stockholder Approval is not obtained on or prior to the Stockholder Meeting Deadline, the Company shall seek to obtain the Stockholder Approval at each special or annual meeting of stockholders of the Company convened after the Stockholder Meeting (but no less than once in each subsequent twelve (12) month period) (each such meeting, a “Subsequent Stockholder Meeting”) until such Stockholder Approval is obtained. In connection therewith, the Company shall provide each stockholder entitled to vote at a Subsequent Stockholder Meeting a proxy statement soliciting the affirmative vote of the Company’s stockholders necessary to obtain the Stockholder Approval at such Subsequent Stockholder Meeting, and the Company shall use its reasonable best efforts to solicit and obtain the Stockholder Approval at such Subsequent Stockholder Meeting and to cause the Board of Directors of the Company to recommend, to the extent possible consistent with its fiduciary duties under Delaware law, to the Company’s stockholders that they vote to approve the Stockholder Approval proposal at such Subsequent Stockholder Meeting.

12. Form D and Blue Sky. The Company shall make all filings and reports relating to the Exchange required under applicable securities or “Blue Sky” laws of the states of the United States following the date hereof, if any.

13. Effective Date. Except as otherwise provided herein, this Agreement shall be deemed effective as of such date as the Company and the Holder shall have duly executed and delivered this Agreement (the “Effective Date”).

14. Miscellaneous. Section 12 of the Securities Purchase Agreement is hereby incorporated by reference herein, mutatis mutandis.

15. No Commissions. Neither the Company nor the Holder has paid or given, or will pay or give, to any person, any commission, fee or other remuneration, directly or indirectly, in connection with the transactions contemplated by this Agreement.

16. Termination. Notwithstanding anything contained in this Agreement to the contrary, if the Effective Date has not occurred and the Company does not deliver the Exchange Notes to the Holder in accordance with Section 1 hereof, then, at the election of the Holder delivered in writing to the Company at any time after the fifth (5th) business day immediately following the date of this Agreement, this Agreement shall be terminated and be null and void ab initio and the Existing Notes and the Existing Warrant shall not be cancelled hereunder and shall remain outstanding as if this Agreement never existed.

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IN WITNESS WHEREOF, Holders and the Company have executed this Agreement as of the date set forth on the first page of this Agreement.