How do you cut down hayto small pieces to put into a compost pile?

You don't. You just layer it in. I've never chopped any of the hay or straw I've used in my compost. It helps loosen the pile as a whole & lets some air into the mixture.

There is a hay knife that was used in the old haystacks--I'm not sure whether making or taking down the stack. It's about 2 ft. long, has a main handle at the end and a second handle--much like the side handle on a scythe, and weighs a couple or three pounds. Nice wall hanger but I wouldn't use it. Baled hay is about the right size to put into the compost pile, for the reasons BG noted.