Dig the ground to expose the roots. Dig a deep trench around the roots.
Pull out roots that are already dead and detached. Sever roots that are still connected with a handsaw. Saws specially designed for cutting roots are available and look similar to a drywall saw.
Break up the trunk and core root with an axe. Hammer the end of a pry bar into cracks and use it to break up smaller pieces. Remove chunks as they detach.
Compost all extracted matter.
Remove any rocks from near the stump and roots.
Position a stump grinder over the edge stump or central taproot. Adjust the height with the hydraulic lever so that the blade sits 3 or 4 inches above the surface of the stump or taproot.
Start the machine and slowly lower the blade, cutting 3 to 4 inches into the stump. Move the blade left to right, using the lever, to clear out chunks. Raise the wheel, move the machine forward and cut into the stump again.
Gradually keep moving the machine forward, removing the stump or tap root and severing the side roots.
Dig up and remove remaining roots by hand. Compost all extracted matter.