A tater rake might not be as much fun but it's way cheaper and way more effective. If you'll start on the backside of the dam and remove the sticks first once you start the water flowing it'll wash out really easy.
If you don't get rid of the beavers you can tear the dam out a thousand times and they'll build it right back.
This X 283849. We get rid of them on the farm for agriculture purpose. But I ain't ever wanted them gone when it came to hunting. Little beaver pond makes for good habitat for lots of different critters.