A handaxe in Middle-earth, is a short-term for a simple one-handed axe. It is not to be confused with a "Stone Hand Axe", a very primitive tool and weapon made of flint or other stone materials.
In Middle-earth handaxes are used by the Beornings, Dunlendings, some Dwarves, Hobbits, Umli and Silvan-Elves, the Woodmen, Woses and some Eriadorian Tribesmen.
The Beornings and Woodmen also use a very large Axe with a broad head known as a Woodman's axe.
Primitive stone handaxes are used by Trolls and primitive tribes of Orcs or Men (the Drûghu, for example).