Hatchet

A Hatchet can be used to harvest Wood Piles in forests and be used as a melee weapon.

The Hatchet is treated as a primary weapon or as a tool. If you want to use it as a weapon, you need a free primary weapon slot. Otherwise, it will just take a tool slot. It is possible to store the Hatchet in your backpack, however it must first be placed into your tool slot and then transferred to the backpack via the standard inventory interface; you cannot directly move a Hatchet from the ground to your backpack.

How to use the Hatchet to cut down wood.
(Vanilla) To use the hatchet you must be in standing next to a tree. Forested areas are designated as green highlighted areas on the map, only there of which can you acquire wood from a tree.

Once you are in the correct location, you can use it to harvest wood by going into your inventory and right clicking it. It will bring up the option to 'Harvest wood'. Clicking this will add a Mod:Wood Pile to your inventory if you are in the correct location and have two inventory slots.

(Epoch) In Epoch, you can simply hack the tree with the hatchet and after a few swings the tree will fall over and yield wood piles. The Chainsaw is a higher-end quicker version of the hatchet that also provides Lumber instead of wood piles at the cost of having to fuel it.

Bugs
When the Hatchet is equipped, it will need to be "reloaded". This is because ArmA 2 does not contain melee weapons, so the mod still requires it to be reloaded because it is technically a gun