Hey, I tried out your game. I noticed that when I'm using the third tool (I think it's a saw), It also works for trees that have been cut down with the axe. So I cut down a tree with the axe, it disappeared, but I can still use the saw on it and get wood.
Also, sometimes when I use the saw on a tree, the character makes a jump or gets pushed back. One time I even got pushed out into the desert a bit.