Although we don’t think of this as a particularly tough neighborhood, this is the second severed head we’ve encountered in the last few years during our routine walks:
We doubt a predator would do such a tidy job of parting the head from the body, then discarding it. The eyes surely went to a bird, though…
It was across the Mighty Wappinger Creek, near the far end of Romca Rd. The Red Oaks Mill Civic Association is long gone and their building burned to the ground a few decades ago, but their name lives on.
The Smell of Molten Projects in the Morning 
A little something for the mantle? I think you’re right, not sure most predators could do that so well. And at least these were found over years and not weeks or days. Anyone mutilating animals to that extent has an especially disturbing problem. But it could just be that someone locally slaughters their own rabbits and these are the convenient pieces to carry off, you were just lucky enough to find them.
It’s not “who”, but “what”, specifically an owl, most likely great horned.
There’s a very long wiki article on them at: https://infogalactic.com/info/Great_horned_owl, but the key bit is:”60% of prey items were found to have been decapitated.[77]” (ref in the wiki article). I gather they’ll go for the braaaaaiiiins! Lots of fat and protein in a handy size. The head was probably (supposed to be) a snack and the rest was taken away for dinner.
My wife found a headless jackrabbit around on our place (we’re very rural with no casual passers by), and we get a bunch of owls of various types on our land, especially the great horned. A local rancher raised emus, and the GHOs would kill them, but leave the body. The good news is they’ll eat skunks, apparently no sense of smell.
The residents sound like Barred (“Who cooks for you?”) and Barn (“Who? Who!”) Owls, but surely a few Great Horned Owls terrorize the rodents, too.
Good hunting to the lot of ’em!
We’ll look for a hutch the next time we walk that way…
I had a neighbor who raised rabbits for food. I never saw how he killed them but decapitation seems as likely a way as any. Could be scavengers are getting into the offal.