You may think your job is completed once you've cut down a tree, but in actuality your job is only half done. If you do not kill and remove the stump and the still-living roots of the tree you've just chopped down, it is very possible that new shoots will grow from the stump or even from the roots. Fortunately there is a relatively simple way of killing and removing roots and stumps in as little as eight weeks, with only moderate effort on your part.
Cut the stump off fairly flat at ground level.
Drill as many 3/8 inch holes in the stump as you can, drilling them as deep as your bit.
Fill each hole with a high nitrogen fertilizer, the higher the nitrogen content the better. Dampen the fertilizer as deep down into the holes as possible. Add more fertilizer to fill the holes to the top and add even more water. Cover the entire top of the stump with the nitrogen fertilizer, dampen it with water and then cover everything with a black plastic sheet. Weigh down the edges of the sheet.
Remove the plastic sheet after eight weeks. The stump should be dead and signs of rotting should be evident. Sweep off any remaining fertilizer and bag it up.
Use a stump grinder (available for rent at most hardware stores and home improvement centers) to grind the stump down to the roots. Grind as deeply as you can, at least 12 inches deep, although once you have ground away the stump the roots will die on their own.
Fill in the hole where the stump was with soil and water lightly.