A mattock is a handheld tool used for cutting tree roots in order to remove a stump. On one end is a chisel-like blade and on the other an axelike blade. The chisel is used to loosen and remove soil and the axe is used to break the lateral and tap roots. Louisiana State University recommends using a mattock to remove stumps that are 14 inches in diameter or less, because a mattock may be ineffecive against larger tree stumps and those with taproots.
Expose the roots. Use the chisel end of the mattock to loosen the soil around the roots and the same end to remove the soil. A shovel will help to remove large amounts of soil and a hand trowel may be useful to uncover the lateral roots as the bulk of the soil is taken away.
Look for the two or three main roots. These are the roots you'll have to sever in order to loosen the stump. Use the axelike end of the mattock and begin making cuts at the tapered end of the roots. Then make a second cut on each root closer to the stump.
Cut as many roots as possible. Leaving smaller roots intact shouldn't hinder the removal process, but if you can handle a few extra swings of the mattock, don't hesitate to chop them.
Use a straight steel demolition bar to lever the stump out of its hole. Stick one end of the bar under the stump and put your weight on the other end to lift the stump. You may need to continue digging and cutting, as some stubborn roots might be located under the stump.
Roll, drag, and slide, or use a winch, to get the stump out of the hole.
Refill the hole with topsoil.
If you're tempted to use a chainsaw, remember that soil will dull the chainsaw blade very quickly. A mattock isn't dulled when it comes in contact with the soil.