The "dirty" use seems pretty silly (sounds like something out of a crass 80's movie or something), but I can't really imagine using it in a non-dirty manner either. I mean I know people have hunted and trapped beavers, but when the capture them they don't just, like, thwack them with a giant cleaver, right? Would ruin the pelt if nothing else.
Not sure if you're messing with me, but Beaver Cleaver is the name of a famous sitcom character. Awesome show IMO, you can watch the entire series for free on archive.org