Simply cutting down a tree isn't enough to kill the roots left underground. Those roots are still alive, which virtually assures that the tree will regrow by sending new shoots out of the stump. Using salt is a cheap and effective way to kill tree roots and accelerate the rotting process of the stump. The best time of year to kill tree stumps is from late May through mid-August. This is when their growth declines as they prepare to enter winter dormancy.
Cut the tree stump down to ground level.
Drill some holes into the sides of the stump near the top of it. Make them as large as you can, and drill them at about a 45-degree downward angle pointing toward the center of the stump.
Pack the holes full of rock salt. The holes will help to circulate the salt through the stump and into the roots, hastening the killing action.
Spread a generous band of rock salt on the ground around the stump. Water it into the soil thoroughly until you don't see any crystals remaining. Then apply another band of salt. This should prevent the stump from growing anymore and kill the roots. Don't put salt on any vegetation that you don't intend to kill.
Cover the stump with fertile topsoil, which contains bacteria that will help to break the stump wood down. Rotting wood in soil attracts beetles and other insects to feed, further assisting the process.