"to chop wood": Abba Shaul says: Just as the chopping of wood is a (merely) "permitted" activity, so, all such activities are subsumed (in the halachah) — to exclude (a mitzvah activity, such as) a father beating his son (to chastise him), etc.
(Devarim 19:5) "and his hand swing the axe": From here it is ruled that if he intended to chop down a tree and it fell on a man and killed him, he is exiled.