Servicemembers and Veterans Prescription Drug Safety Act of 2013

Servicemembers and Veterans Prescription Drug Safety Act of 2013 - Directs the Secretary of Defense (Secretary) and the Attorney General (AG) to jointly carry out a program under which a member of the Armed Forces (member), an individual receiving or entitled to military retired or retainer pay, a dependent-beneficiary of a member, or any person lawfully entitled to dispose of the property of any of such individuals may deliver a personal-use controlled substance (the prescription medication of a deceased individual) for disposal at a facility to be specified by the Secretary and the AG. Requires the Secretary and AG, in implementing the program, to develop appropriate guidelines and procedures to prevent the diversion, misuse, theft, or loss of such delivered substances.

Directs the Secretary and the AG to jointly carry out a program under which a veteran, a veteran's spouse or dependent, a person in receipt of medical services at a Department of Veterans Affairs (VA) facility, or any person lawfully entitled to dispose of the property of any of such individuals may deliver such a controlled substance for disposal at a specified facility, subject to the same guidelines and procedures with respect to such delivered substances.