Ofcourse it is possible.
One of the ways to do this is to have an imagepoint on the axe and spawn an invisible axe-collision sprite when attack animation is playing at that imagepoint and deduct health from your enemy when the axe-collision sprite collides with the enemy.
Dont forget to destroy the collision sprite on attack animation end.
There are more ways to do it, but as this one is probably the most easy to understand, I offer this one.