There are several ways to remove cut tree stumps. The best method depends on how much time you have and the size of the stump. Trees that have a 12-inch girth or smaller are much easier to remove by hand. Sometimes, a tree must be removed because it died and is rotting, or because of extensive damage from storms.
Allow the tree stump to rot, if there is no hurry to remove it. Until the stump rots, you can camouflage it by using it as a plant stand, or otherwise incorporate it into the landscaping. Rotting wood attracts some types of insects, and provides a natural "live" bird feeder. To encourage faster rotting, temperatures should be between 50 and 90 degrees Fahrenheit, and the stump should be kept moist. Drilling holes and adding nitrogen-based fertilizer to the stump also hasten decay.
Pull stumps out by hand. This is known as "grubbing." Dig a 2-foot-deep and 2-foot-wide trench around the stump. Cut the roots, using the ax. If the tree has a taproot, wrap a chain around the stump. Attach the winch to the chain, and pull the stump to the side. Using the ax, cut the taproot. Fill the hole with topsoil.
Burn the stump. Before burning, check your city or county ordinances for burn permits. Dig a 2-foot-wide trench around the stump, and put a fireproof fence around the stump (stone works well) to prevent the fire from spreading. It could take up to two weeks to burn out a stump because of the low availability of oxygen in the root ball.
Punch 1-inch draft holes in a metal can that is large enough to fit over the top of the stump. The holes need to be on the sides of the can, and near the bottom. Remove the cover and the bottom of the can. Set the "stove" on top of, or over, the stump. Start a fire in the stove. If the stump is large, and you cannot find a can large enough, use what you have. Move the can from the burnt part of the stump to the unburned part of the stump. Repeat until the stump is completely burned.
Remove a stump using chemicals. Though the chemicals take some time to work, and might have to be reapplied, they work faster than allowing the stump to rot on its own, and are safer than burning. Chemical stump remover is found at nurseries or big-box home and garden stores. Commonly used chemicals include potassium nitrate, sulphuric acid, saltpeter or nitric acid.
Grind the stump out with a stump grinder. You can rent a stump grinder from a big-box home and garden store that has a rental department, or your town might have a business that rents large equipment. Grinding stumps leaves holes in the ground. Fill the holes with topsoil.