Interesting game! Nice take on the theme, good mechanics. Music gets repetitive pretty fast as the loop is quite short. An option to turn that off would have been welcome!
The axe mechanic is also fairly novel, I haven't seen anything quite like it before. I like how you can only double jump when not carrying the axe, and that you can retrieve it from wherever it ends up quickly. I also like how flexible it is - you can throw it downwards from a jump to make a springboard. You can throw it diagonally up to kill enemies above you etc.
I didn't like going all the way back to the start when I died however, and I gave up after falling to the start area from a tricky tall platform above it. I was wondering if checkpoints would have helped, but I can tell you're trying to ape Getting Over It with it's non-failure failure modes! You just lose a load of progress. It mostly works in that game, but I'm not so sure about a games jam where nobody is as invested in getting to the top.
I'm probably too old to be able to play this well. I couldn't get used to the controls enough to react to the twitchy movement, although it is very well done. It's just not for me, but that doesn't harm my rating of it. Overall, great effort!