Too bad it wasn't 50 years earlier. You could go down to your local hardware store and get a box of dynamite and toss a stick into the dam every year. After few years they will move on.
Then again everyone has diesel and almost anyone can their hands on fertilizer. ;-)
Wedge
ANFO! Kaboom!
Anyhow we have an earth dam and the beavers and muskrats do some pretty severe damage to it if left unchecked. DNR says don't shoot the beavers, but nothing here eats them, so that is where we came up with the expression shoot, shovel, shut up. We have been beaver free for about 3 years now, its nice not having to deal with the destructive little pests.
Also there is nothing serene or more natural about a beaver dam than a man made one. Beavers dam up water to make a high side and a low side, if the low side isn't draining they go down stream and destroy what ever other dam is in the preventing the draining. They are just like man shaping their environment to what they want. If they were equal to man they would have little beaver rifles and shoot back, lucky for us they are just giant rats.
On to the topic of shooting animals.
I kill and eat deer they are tasty destructive pests, and they are so over populated here there are over 200 deer car accidents every year on the 20 mile stretch of highway I live on. Last year almost 100,000 tags to hunt were issued (2 per tag) and the population still expanded.
I kill and eat turkey and snow goose (snow goose are destroying much of the northern tundra due to overpopulation).
I kill and leave to rot nuisance animals like possums, coons, muskrat, and beaver because they are destructive or disease vectors and natural predators for the most part don't exist.
I take a prairie dog hunting trip once a year because I am a sicko and I love watching the little guys explode when hit with my 22-250.