i don't know if its legal or not but why not just call animal control. it would take care of your problem and chances are the beaver would have a chance to live.
It's best - legally and morally - to simply call animal control . They'll take care of the situation or at the very least point you towards an agency who will . The beaver are only doing their job - no need to shoot them . Call animal control - in yellow pages or on the net - and they'll attend to it.