Servicemembers and Veterans Prescription Drug Safety Act of 2017 This bill directs the Department of Defense (DOD) and the Department of Justice (DOJ) to carry out a joint program under which an eligible person who has lawfully obtained a covered controlled substance may deliver it for disposal at a facility to be specified by DOD and DOJ. An eligible person for this purpose shall be: a member of the Armed Forces, an individual receiving or entitled to military retired or retainer pay, a member's dependent-beneficiary who is receiving certain health care services, or any person lawfully entitled to dispose of the property of any of such individuals who dies in lawful possession of a controlled substance for personal use. DOD and DOJ shall develop guidelines and procedures to prevent the diversion, misuse, theft, or loss of such substances delivered under the program. DOJ and the Department of Veterans Affairs (VA) shall carry out a similar joint program covering any veteran, veteran's spouse or dependent, a person in receipt of medical services at a VA facility, or any person lawfully entitled to dispose of the property of any of such individuals who dies in lawful possession of a controlled substance for personal use. DOJ and the VA shall also develop guidelines and procedures to prevent the diversion, misuse, theft, or loss of such substances delivered under the program.