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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-05-18</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001722992</issuerCik>
        <issuerName>Spirit MTA REIT</issuerName>
        <issuerTradingSymbol>SMTA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001308606</rptOwnerCik>
            <rptOwnerName>SPIRIT REALTY CAPITAL, INC.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2727 NORTH HARWOOD STREET, SUITE 300</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001739743</rptOwnerCik>
            <rptOwnerName>Spirit General OP Holdings, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2727 NORTH HARWOOD STREET, SUITE 300</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001703181</rptOwnerCik>
            <rptOwnerName>Spirit Realty, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2727 NORTH HARWOOD STREET, SUITE 300</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common shares of beneficial interest</value>
            </securityTitle>
            <transactionDate>
                <value>2018-05-18</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>42851011</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">On or about May 31, 2018, Spirit Realty Capital, Inc. (&quot;Spirit&quot;) will make a pro rata distribution of 100% of the outstanding common shares of the Issuer to Spirit stockholders of record as of May 18, 2018 (the &quot;Distribution&quot;).  On or prior to the date of the Distribution, SMTA will recapitalize the SMTA common shares then held by Spirit Realty, L.P. such that Spirit will distribute to its stockholders one SMTA common share for every ten shares of Spirit common stock held by stockholders of Spirit as of the close of business on May 18, 2018.</footnote>
        <footnote id="F2">Reported number of shares reflects the recapitalization of the SMTA common shares that is expected to occur on or prior to the date of the Distribution based on the number of shares of Spirit common stock outstanding as of the close of business on May 18, 2018.</footnote>
        <footnote id="F3">The shares will be directly owned by Spirit Realty, L.P. until immediately prior to the Distribution. Spirit General OP Holdings, LLC, a wholly-owned subsidiary of Spirit Realty Capital, Inc., is the general partner of Spirit Realty, L.P.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Spirit Realty Capital, Inc. By: /s/ Michael Hughes, Executive Vice President, Chief Financial Officer and Treasurer</signatureName>
        <signatureDate>2018-05-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Spirit General OP Holdings, LLC By: /s/ Michael Hughes, Executive Vice President, Chief Financial Officer and Treasurer</signatureName>
        <signatureDate>2018-05-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Spirit Realty, L.P. By: /s/ Michael Hughes, Executive Vice President, Chief Financial Officer and Treasurer</signatureName>
        <signatureDate>2018-05-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
