I suppose you have tried to trap and or shoot 'em?
Beavers are like cockroaches. The only way to make 'em stop is to stop them.
A rather liberal tree hugger type of guy down the street had a family (One lodge) of beavers in his pond. He thought it was so cute. They were cute till there is now three lodges and they have damned up the outlet of his pond to the point that the pond is creeping closer and closer to his house.
Well he blew up the damn which caused property damage down stream of him. Once he took care of his neighbor'$$$ he bought a "Hav-a Heart" trap. Trapped some of them and moved them out of the area. Got caught by a Environmental Officer and got a ticket on his third trip to the State Game Lands - Again some more $$$$.
Well he has resorted to my original suggestion which costs nearly nothing - He shot 'em.
He sat on his porch at dusk several months ago and dispatched what he thought was the right amount. No fuss...No musss. Since gunfire is very common around these parts and there is only one Environmental Officer who only hangs out at the state game lands. Nobody is the wiser