In 1974, the FBI responded to Nebraska Senator Curtis that they were unable to investigate cattle mutilations due to a lack of jurisdiction- the cattle had not been moved across state lines. They provided a similar response to Colorado Senator Haskell (Animal Mutilations part 1).
In 1979 there were reports of mutilations on Indian Reservations in New Mexico that this fell within the FBI’s jurisdiction. An investigation in New Mexico resulted in Operation animal mutilation: report of the district attorney first judicial district, state of New Mexico Kenneth M. Rommel, 1981. In the 1980s theories on the possible culprits included Satanists, witches, pranksters, unknown government agencies, and extraterrestrial visitors (see part 5 of 5).
The FBI Vault has reports, correspondence, and news clippings.