<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0407</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-04-28</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001836056</issuerCik>
        <issuerName>Ambrx Biopharma Inc.</issuerName>
        <issuerTradingSymbol>AMAM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001976455</rptOwnerCik>
            <rptOwnerName>Aromando Andrew</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O AMBRX BIOPHARMA INC.,</rptOwnerStreet1>
            <rptOwnerStreet2>10975 TORREY PINES ROAD</rptOwnerStreet2>
            <rptOwnerCity>LA JOLLA</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92037</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Operating Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.38</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-04-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2600000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2033-04-28</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Ordinary Shares</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2600000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2600000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The options will have an exercise price per share equal to the fair market value per ordinary share on the grant date based on the trading price of the Issuer's American Depositary Shares (&quot;ADSs&quot;).</footnote>
        <footnote id="F2">Grant awarded as an inducement grant in connection with the Reporting Person's appointment as Chief Operating Officer of the Issuer.</footnote>
        <footnote id="F3">Twenty-five percent of the Ordinary Shares subject to the option vested on April 28, 2024, and the remainder vests in thirty-six equal monthly installments following such date.</footnote>
        <footnote id="F4">The Ordinary Shares of the Issuer may be represented by ADSs. Each ADS represents seven Ordinary Shares of the Issuer.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Sonja Nelson, Attorney-in-Fact for Andrew Aromando</signatureName>
        <signatureDate>2023-05-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
