Veterans Mental Health Treatment First Act - Directs the Secretary of Veterans Affairs to carry out a program of mental health care and rehabilitation for veterans who: (1) are diagnosed by a Department of Veterans Affairs (VA) physician with post-traumatic stress disorder (PTSD) or depression, anxiety, or substance abuse that is either related to the PTSD or service-related; and (2) agree to participation conditions, including compliance with a treatment regimen and rehabilitation plan prescribed by the Secretary of Veterans Affairs. Requires each participant to be paid a stipend during successful program participation, limiting to $11,000 the total stipend paid to each individual.