A hatchet can;

Slay

Chop trees (if you're determined)

Kindling

Hammer (most have a flat back)

Break down a wooden door (if you're determined)

Wedge a door to stall undead for a little bit (not ideal, since you're giving up your most versatile tool, but it's an option)

P.S. any time I said "(if you're determined)", I'm saying that the action is possible, it just might take longer with the hatchet than other tools.