Don't use rope, unless its made out of steel. The way I prefer to rig both snares and foot hold traps for beaver and other water dwelling critters is with a drowning setup.

If this doesn't look like an option, then depending on the soil, you may need to use a rebar stake at least 2 ft or better yet, cross stake, removing all doubt that it will hold. Use at least 11 gauge wire, 9 gauge would be best for fastening the snare to the stake.

I prefer to have the animal out away from trees and brush to keep from entanglement and ultimately a lost animal. And in the case of beavers, if it gets away and survives, it will become educated and as difficult to catch as some coyotes.

Drowning setup explained.....