I been shootin beavers since i was a lil gaffer prolly shot more than most people ever see lol.Mostly they do butsometimes they don't. The majority of the time they will float so i either hookem with a fishing hook and dragem in or get a big stick or a hook to reach out and get them. I have swam for them before but i really detest doing that. When they do sink it is usally because they are still slightly alive, nerves or whatever and they go into what i call is the death spin. They spin around thrashing and kicking and eventually sink. If the beaver is stone dead when hit I have never had one sink. Maybe 1 in 10 sinks on me however like previously said they may float up the next day so keep an eye out. Also if they are wounded they may go down, grab hold of a root, or burry themselves under a log and die. If they do sink go over to where they sank, sometimes they are suspended in the water and you can see their tail only bout a foot under the surface. good luck
