Beavers have special protection under game laws and you will probably have to get a permit to remove them. Shooting is not likely allowed.

My Grandfather who was an Adirondack native Indian used to say that if you needed meat the best way to get it quickly was to find a beaver dam, open up the flowage and wait with a club. This especially true in winter when water levels needed to be maintained to ensure their survival.

That being said, beavers are most active at night. You can dynamite the dams and destroy the lodges and they will move on. BTW, more Game Wardens in Maine have been killed while destroying beaver dams than by any other hazard they face.

Good Luck.

Drew