Wood working, I sure hope it does!

Well, yes but also no. Depends entirely on the density of the wood making up the axe and the tree you want to chop down. It'd be a massive pain to do even if you did it right but you could do it. The heartwood of a super dense ironwood tree would need to make up the blade. It'd also have to be huge cause even properly treated it wouldn't hold an edge and you'd have to constantly resharpen it. The tree you cut down would have to be light, probably Balsam or something similar.

Have ya ever seen or played Minecraft? Of course it can