I do have some tips, maybe I can share lil bit here :

1. Build some trap, by 2x2 stone block

2. Agro the beaver into the trap, its easier if U do have the

Argentavis.

3. Of course u need a stunt gun, like Tranq Arrow or similar

like this.

4. After U lock him up into the trap. just leave it for lil bit,

dont knock it down yet (when he starving/0 food and

can't harvest some food because the trap).

5. Then, knock it down after a few minutes. and then put

food with a cheaper one like Mejoberry's. it will force him

to feed because he very hungry (don't do by ur self, let

him eat automatically). *better with Kibble

5. And Tadaaa, congratulations for Ur Wooden Chopper

Machinaa.

note : U can skip the part 3, but. U must bring a lot of some

Narcotic, because this thing have some big torpor.