I burned down a small forest of evergreens near base to harvest charcoal. When chopping down the burnt trees, a few of them became inactive, and could not be cut. In the video, I tried switching between two axes, but it didn't solve the issue. I also waited until the next day, increased my sanity back up, and tried to chop the burnt tree without success. I didn't try using a shovel (I don't even know if it's possible to dig up a burnt tree).
I hopped into the same world server (wilderness, offline, 2 player max) as a new character after and found that the burnt trees erased themselves off the base.
Plant a small remote forest of evergreens, burn them down, cut and harvest all the trees.