The mattock tool, which dates back to before the 12th century, is related to the ax. It's considered a "digging and grubbing tool," with features similar to that of an ax or pick, according to Merriam-Webster. You'll find mattocks in a variety of shapes and sizes with most having a flat blade on one side, and a pick on the opposite side. Mattocks seem suited for stump removal as you can use one end to cut the deep tap roots and the various lateral roots that extend from the tap root. Use the blunt end for leverage and force.
Dig a trench with a shovel around the base of the stump that is 1 to 2 feet wide by 1 to 2 feet deep.
Hit the lateral roots with the sharper end of the mattock. Move the stump to one side and cut the tap roots with the mattock's sharp end.
Slide the stump out of its hole. Place the mattock's blunt end underneath the stump and push up on the stump to force it from the ground.
Drill 1-inch deep holes around the perimeter of the stump if it does not remove easily or if the roots are too difficult to cut. Space the holes evenly. Pour a stump removal chemical into the holes. Break up the stump with the mattock after it decomposes, which becomes evident when it feels spongy.