Biological Implant Tracking and Veteran Safety Act of 2017 This bill directs the Department of Veterans Affairs (VA) to: adopt the unique device identification system developed for medical devices by the Food and Drug Administration (FDA), or implement a comparable standard identification system, for identifying biological implants intended for use in VA medical facilities; permit a vendor to use any of the accredited entities identified by the FDA as an issuing agency; implement (within 180 days after enactment of this bill) a compatible system for tracking implants from human donor or animal source to implantation; and implement compatible inventory controls so that patients who have received a biological implant in a VA medical facility subject to FDA recall can be appropriately notified. The bill prescribes requirements for vendors from which the VA may procure biological implants of human and non-human origin. The VA shall: (1) procure such implants under General Services Administration Federal Supply Schedules unless they are not available under such Schedules, (2) accommodate reasonable vendor requests to undertake specified outreach efforts to educate VA medical professionals about the use and efficacy of implants, and (3) procure biological implants that are unavailable under such Schedules using competitive procedures in accordance with the Federal Acquisition Regulation. Certain biological implants may be temporarily procured by the VA without relabeling under the standard identification system.