Cut the willow tree trunk with a saw. Measure 6 inches up the trunk from the ground and make a horizontal cut with the saw completely through the trunk.
Drill vertical holes into the top of the willow stump with a drill and bit. Use a drill bit that is 1 inch in diameter. Drill the holes 10 inches deep. Drill one hole for stumps that are 4 inches in diameter or less. Drill additional holes in larger stumps.
Drill holes along the side of the stump from the cut, down to ground level with the drill and bit. Measure 6 inches down the trunk from the cut. Drill the holes on the side of the trunk at a 45-degree angle and at least 6 inches deep.
Add chemical stump remover to the holes in the top and sides of the trunk, following the manufacturer's directions. Allow at least six weeks for the chemical remover to work.
Pour kerosene into the holes on the top and sides of the trunk. Carefully light the kerosene and allow the stump to burn and reduce to ash.