The tree is gone, but the stump is not. Now it's just an eyesore and you are pondering how to kill it so you can remove it. You can use a chemical or natural approach for killing a stump. Most methods for killing the stump work fine, but some take longer or require more labour.
Kill It With Chemicals
Stump removal chemicals break down the surface of the stump into a spongy textured material that you can easily break up with an axe. Apply the chemical to the stump by drilling a series of holes into the top. Pour in the chemical and wait for decomposition to start. It usually takes a few weeks for the stump to reach the spongy condition, but there is little work involved except the application and easy removal afterward. Stump remover is available at garden and home centres.
Burning is another option to kill the tree stump. It's more dangerous, one you must prepare for appropriately to protect surrounding structures, children and animals. To start the fire, set wood logs and any brush on top of the stump to get a hot fire going. Allow the fire to burn until it burns the stump to the ground. Keep the stump enclosed with fencing to keep children and animals away from the fire. This should also contain the fire somewhat, but you still need to watch it closely so it doesn't spread.
Let It Decay
Natural decay slowly kills the stump over a period of several years. Sever the roots first with an axe to cut off the stump's lifeline. The stump may continue to grow new suckers, but to keep the decaying process going, cut back this growth as it appears. This natural method can take as long as 10 years to completely kill off the stump.
Stump removal chemicals are hazardous, so handle them carefully and wear gloves. Avoid breathing in chemical fumes or getting chemicals on your skin or in your eyes or mouth. Because burning the stump could spread and cause a grass fire, check with city burn ordinances on whether burning is permitted in your area.