You may be able to hire an outside trapper to come in and do the job for you. They will kill the animals for their pelts. This is a point where you have to make a choice--beavers are hard-headed about continuing to build. I have seen huge trees in forests in Washington State that they tried to gnaw through (trees upwards of 3-4 feet through!). There really isn't a pretty way to deal with the population except to trap them live and relocate them, thus giving the problem to someone else.

SRS