A question about constraints

Is it possible to remove constraints in the middle of an animation? How?

I am wanting to have a sword fight and one of the characters throw their sword and stab the other and make it stay in his head…

is there a better way to do that than constraints?

You can key the influence of constraints. Just key them from 1 to 0 over the course of 1 frame. That essentially “switches” them off.