Using an axe takes a lot of practice and occasionally along the way handles get broken. This usually occurs when the head misses the target and the handle takes all the force from the blow. To remove a broken handle, the easiest way is to put it in a fire, burying as much as possible of the metal in the earth (to prevent it losing temper).
Never attempt to repair an axe handle.
Never use any axe that has a damaged or split handle.