Nice idea for a tricky platformer! It's very challenging and I like it quite a lot, sticking the sword into walls as a main gimmick with that physics-based movement really makes the game feel unique and fun. Though sometimes it may feel a bit unfair as the strength varies a lot depending on how the sword was placed, and I do fall quite a few times because of this. I guess this is very intended though. The collectable stars are also a nice touch to an otherwise awesome game.
I'd admit after playing for quite some time my hand hurts a bit from constantly clicking and dragging, so I stop at somewhere around level 8, but I am sure it's only able to get better (and harder) from here.
Good game you've made here! Well done!