Battle axe
From Dwarf Fortress Wiki
A battle axe is both a weapon and a tool for wood cutting. Without at least one battle axe, your fortress will be unable to cut down any trees for wood. Axes can be made of silver, copper, bronze, bismuth bronze, iron, steel, as well as adamantine; all axes are equally good at cutting down trees, but stronger metals or those of higher item quality will do more damage in combat (see Weapon Stats).
Wood cutters who immigrate to your fort will (usually?) come with an axe of some type. When starting a new fort, however, you must "buy" axes out of your starting points for your woodcutters. An alternative is to take needed materials and forge axes on site; this is cheaper than buying the actual axe, if you are going to bring along the anvil anyway. The only axes available on embark screen are steel ones, which are expensive at 300 currency each, and are standard quality (the lowest).
As a weapon, battle axes do "slashing" damage, which severs limbs and causes bleeding. Axes can be used with a shield.
Any dwarf that performs wood cutting will pick up an axe (if one is available) and not put it down until they are no longer assigned the Wood Cutting labor. You can make use of this to arm many or all of your non-military dwarves with axes, although if you designate a section of trees for wood-cutting (d, t), all those dwarves will soon rush out to cut them down.
