Not a Bug - Damage Reset

[MarkVM]

I'm not sure if it's a bug but it doesn't seem necessary and is just annoying. When woodcutting it'll reset the damage dealt when you quit to the map and go back.

[CRIMSONKING]

lol Hit the big x on the woodcutting screen instead of quit. In that way you don't lose any progress on the current tree. Quit...means you quit. You give up lol. I know it's kind of silly but maybe the trees 1 hp is too much for you to wait for the timer, so you feel the need to give up and move on to another tree. :p

[Ray]

Correct. Quit is to leave that specific forest area (and forget to leave a breadcrumb trail back to it) to return to forest selection. To come back to it, hit the green X at the top right and your progress will remain.