I too like the idea. The game looks really nice, the music is great and the atmosphere is top notch.
I finished the game so I can tell you there are 24 levels in all.
And now the beef.
1) On many levels I didn't have to use all the cuts and kind of cheated not having to fill up all the areas, just fit the sliced up block where I could. To me that kind of defeats the purpose. This goes hand in hand with my next beef:
2A) The shape area on the right is sometimes too big which allows for solving the puzzle in a different way than intended (I understand some room is needed because the cuts are not perfect) and
2B) it's superannoying when everything is inside the lines but it still won't complete. This means that the borders are very inaccurate. This could also be improved immensly by highlighting what exactly is "outside" the border since I couldn't tell a few times and just started over.
3) The pieces stick to each other in a very annoying way. Sometimes you can get them close to each other, sometimes you can't close the gap and sometimes you can't move them up or down between two pieces and you have to move the other pieces first.
4) Though I like the analogue feeling of the cuts as it goes hand in han with being a swordmaster - it has nothing to do with intelligence when you know what cuts you need to make, but have to restart countless times because of the inaccuracy of the cuts. Even when you line it up straight down the middle the resulting pieces are different sizes. This to me is just tedious and annoying.
Here is what you could do if you make a sequel - because despite of above comments - I enjoyed the game and would like a more puzzling sequel.
Make the block slices line up in an absolute grid of say 10x10 so the cuts are always perfect and the solution as well. It can still look analogue, but you either solve it correctly or you don't and there will never be an issue of "cheating" or being outside the shape lines as everything should lock into place like tetris blocks. For more difficult levels you can make the grid bigger so you get 15x15 block to chop up and so on. This would solve all the above mentioned issues.