The mutilated remains of a deer were dumped near a woodland shrine devoted to Sir Paul's McCartney's late wife Linda, police have confirmed.
Linda McCartney was an outspoken champion for animal rights
The head, legs and intestines were found last month on a road adjacent to Sir Paul's estate near Bampton, on the Somerset-Devon border.
The League Against Cruel Sports, which manages the site for Sir Paul, believes pro-hunting groups may be responsible.
"The depravity of this is appalling," league spokesman Paul Tillsley said.
"For it to have been committed on land dedicated to Linda's memory is all the more shocking."
The league said the site had been targeted in the past.
Lady McCartney, who died in 1998, was a well-known advocate for animal rights, lending her support to organisations including People For The Ethical Treatment of Animals (PETA), which Sir Paul continues to support.
Avon and Somerset Police said officers had been contacted by the league, but no crime had been reported as there was no information as to who was responsible.