The skinned remains of a sheep have been found in Felbridge, Surrey with police linking two other similar incidents in the area.
Councillors have raised the issue that livestock are in danger of being killed for cheap meat.
Local farmers said the number of their sheep was correct meaning the animal was taking further away.
It is the third time in five months that animal remains have been dumped in the area, with deer bodies being discovered in January and November last year.
Tandridge District councillor for Felbridge, Ken Harwood said it was one of these things where you think 'what on earth are people up to?'
"The head had been chopped off the body but was still attached to the fleece. Obviously someone has killed a sheep and skinned it.
"There may have been other body parts present when the fleece was originally dumped, but it is likely they would have been taken by foxes or another animal."
'Suspicious activity'
Police have confirmed all three animal incidents are being linked.
"The idea of chopping a sheep's head off, taking the body away and just leaving the rest on the side for anybody to walk by - it could have been a child walking past it," said Harwood.
"Could you imagine a child saying 'mummy what's that?' and the response could only be 'oh don't worry dear it's a sheep sleeping'."
PC Alice Bennett, wildlife and rural affairs officer for Tandridge, said: "At this time, the owner of the sheep has not been identified.
"I would be keen for local farmers to check their flock numbers and report any suspicious activity."
