I have an area on the lower part of our property that the beavers flooded. I filled out the form on the DEC site and got a Nuisance Beaver Permit. It was actually pretty simple, and it allows me to deal with the problem myself, which I've been doing. Per the permit, you can shoot them whenever you want, but if it is not within the normal season, you're supposed to dispose of the carcass, not do anything else with it.
I was pretty pissed about it when I first noticed the area flooding, as it happened in an area that was good deer hunting land before the beavers flooded it. but it seems that the deer movement is now almost funneled into an area where my neighbor put up a two-man stand. I have a trail camera near there that shows a lot more activity now than before the beavers did their thing.
Beavers are more active mornings and evenings, and they know when the dam is leaking, so you can use those to your advantage in getting rid of them.
