Veterans Mental Health Treatment First Act of 2013 - Directs the Secretary of Veterans Affairs (VA) to carry out a program of mental health care and rehabilitation for veterans who: (1) have been discharged or released from active-duty service under conditions other than dishonorable for no more than two years; (2) are enrolled in the VA system of annual patient enrollment and were so enrolled before the date of enactment of this Act; (3) are diagnosed by a VA physician with post-traumatic stress disorder, depression, anxiety disorder, or substance use disorder that is service-related (as determined by the Secretary or a VA physician); and (4) agree to certain participation conditions, including not submitting a claim for veterans' disability compensation for any such condition until either one year after program commencement or the conclusion of the prescribed treatment regimen.

Requires the Secretary to provide for each participant a treatment regimen and rehabilitation plan for the determined condition.

Provides a stipend for participants, commencing upon program commencement, continuing through successful treatment and plan compliance, and ending either upon the conclusion of such treatment or one year after treatment and plan commencement. Allows a veteran to participate more than once in the program if the Secretary determines that the additional participation will assist the veteran in achieving the remediation of the condition.