Welcome Big Luke,
You're right, the beavers will cause big problems if not taken care of. Talk to Bob Lusk or Dave Davidson and many others on this site for the best info.
Check your local wildlife regulations but as far as I know, trapping and or shooting seem to work the best. Beavers are primarily nocturnal so you'll have to get them at night with a red spotlight. Can you find their lodge? If so destroy it and maybe they'll get the hint and move on. I did that on my neighbors place a couple of weeks ago and the beavers left post haste!
