Very interesting, when I read the description I thought it was to be something like Toodee and Topdee, but controlling the top down character with the platforming one is quite clever :)
I liked the minimalist approach too. I would suggest to add some particles or some squish tweening when jumping: it would maintain the minimalism but also increase the game's polish a little in my opinion. Also, the saw was a bit too slow maybe, but that might be just for me. Cool idea and entry!