Carl,
I don't know the first thing about beaver dams .... but maybe you could try removing a few sticks at a time rather than trying to get the whole darn at once. Just a thought.
Either that or there's this really cool beaver dam removal stuff I done heared about. Its called "Dynamite." I heared that it works real good at removing lots of other unwanted stuff, too. Like Edgar Montrose on the Red Green Show (where one can learn how to do all sorts of things...)