Armed Forces Endangered Species Exemption Act This bill establishes exemptions from the Endangered Species Act of 1973 (ESA) for defense-related operations. First, the bill prohibits the U.S. Fish and Wildlife Service (FWS) and the National Marine Fisheries Service (NMFS) from designating military installations or state-owned National Guard installations as critical habitat under the ESA. It also prohibits FWS and NMFS from designating other lands, waters, or geographical areas as critical habitats if the Department of Defense (DOD) determines that the areas are necessary for military training, weapons testing, or other reasons. While DOD must submit such determinations in writing to the FWS, DOD is not required to consult with the FWS under the ESA about such determinations. Next, the bill exempts military personnel engaged in national defense-related operations (actions or duties that DOD deems necessary to support its mission) from ESA prohibitions on (1) taking (e.g., harming or killing) of endangered species or threatened species; (2) importing or exporting such species; and (3) damaging, destroying, removing, cutting, or digging up such species. Further, the bill exempts any injury to or mortality of a threatened or endangered species that results from, but is not the purpose of, a national defense-related operation. The term military personnel means a member of the Armed Forces as well as a civilian employee or contractor of (1) DOD; or (2) any other federal agency, or any provisional authority, to the extent such employment relates to supporting the mission of DOD overseas.