I had fun with this!
Bouncing the axe was enjoyable, especially when it chained between a bunch of enemies.
I feel like it could be improved by some kind of defensive mobility option though.
Perhaps a dodge roll? A micro-dash? The ability to sprint (but only when you're not carrying the axe? Or maybe only when you are?)
I think that would elevate it, and let you design some more aggressive enemies because the player would have the tools to avoid their attacks, which might fit the sort of action arcade vibe I think you're going for?