What is killing small birds in your yard their heads are gone?

It's probably a hawk. They are known to snatch smaller, slower birds and take them into a tree and eat them. Almost certainly not a hawk, they would consume the entire bird, most likely a mammal predator, like a weasel or house cat.

I stand by my answer. I spoke with a friend who raises chickens and she said it is definitely hawks, she watched them do it. She also said that she has a friend who is a ranger in the Great Plains of the US and that it's a problem with hawks killing and eating the heads off of wild pheasants.