FIH, if you need to use a leg hold trap (the way you used the 330) you have to make a drowning set 'cause they will either chew thru the wire like you found out, or will pull up the stake. In any case, pulling a beaver out of a hole while it's still alive is dangerous. They WILL bite.
Once I set a trap for a muskrat (in it's run where it came out from the bank) and I barely had it set and it came out of the hole. I immediately reached for the trap and was lucky that when it tried to bite my hand, it bit between my fingers. Lesson learned - they don't die immediately - it might take them a while. Not to sound cruel, but the trap could break their back and they drown if they're moving fast enough. I've caught 'rats by the hindquarters after they've almost gone thru a 110. I don't know if the trap was slow, or the 'rat was fast.