Your method for removing a large tree stump depends, in part, on the type of tree and its location. Oak trees have hard wood and a deep taproot that goes straight down, making removal difficult. Pine trees have softer wood and shallow, spreading roots. If the stump is located on a new construction site, you can easily bring in equipment such as a backhoe or skid steer to pop it out. These machines will make a mess of small, established yards, though, and you'll need a different solution.
Drill 1-inch holes around the top perimeter of the stump 4 inches apart and 12 inches deep with your electric drill. Drill more holes 3 inches from the top of the stump, along the sides, to intersect with the previously drilled holes.
Fill the holes with powdered postassium nitrate stump remover. Fill the holes with water to activate the chemical. Wait four to six weeks until the stump is soft and mushy. Chop up the stump pieces with an ax. Pick them up with your hands to remove them.
Rent a stump grinder from a hardware or home store. Bring the stump grinder up to the stump and turn it on. Release the handle to lower the grinding wheel so it rubs against the stump. Move the handle back and forth slowly. The grinding wheel will grind 1/2 inch with each pass. Continue grinding until the stump is ground 12 inches below the soil surface. Cut out and remove any remaining wood with an ax. Clean up and dispose of the mulch.
Rent a skid steer. Lower the teeth of the skid steer bucket into the ground to loosen and pop the trunk out of the soil. Bury the stump on your property or take it to a landfill.