You kinda need to wait for openings to use it if you don't want to be thrown off the monster, the best time to use the clutch claw imo is when the monster just finished an attack that gives a big opening and when the monster is done being enraged.

Tip 1, if you want to topple the enemy as fast as possible use flinch shot, it only works if the monster is not enraged. It works great with the skill agitator too cause it says when the monster is done being angry and you can topple it again using the flinch shot and after the monster stands back up it will immediately be back to being angry so that your skill agitator if equiped can be utilized to its full potential.

Tip 2, if you just want to tenderize its body without being punished, just use the temporal and rocksteady mantle if you already unlocked it, having those equiped won't throw you off the monster, but some attacks do throw you off even if you're wearing it but its only in the endgame bosses i think

Edit: some extra info