She took photographs of the remains and posted the images to Facebook.
"I was absolutely over it all. However, now that SPCA inspectoral services have resumed in the Wairarapa, I really hope to see a huge decrease in this appalling behaviour," the woman said.
Senior Sergeant Gordon Crawley said there had been a spate of stock thefts reported to police ahead of Christmas last year and he was not surprised at the reported prevalence of carcasses dumped in or beside waterways in the region.
He was aware of a sign posted near a rural riverside warning "whoever the dirty buggers are" to stop dumping carcasses at the place.
"It wouldn't surprise me [that] people would be dumping carcasses and offal around rivers, to be brutally honest, and it's possibly stolen stock," Mr Crawley said.
"We did have a spate of people stealing stock pre-Christmas," he said.
Police at the time had warned rural people to be alert after six ewes and four lambs were stolen, and possibly butchered, at a Blairlogie farm, and a calf was butchered near the roadway on a Stronvar farm.
The incidents had happened about the same time.
Masterton police Senior Sergeant Mike Sutton said there had been no reports of stock thefts since Christmas but often "the odd sheep" lost to thieves can go unnoticed and the crimes remain under-reported.
He urged rural people to report any suspicious behaviour to police.