Drill several holes into the tree stump at least 6 inches deep.
Pour fertilizer into the holes. The nitrogen in the fertilizer helps feed fungus to break down the wood. Cover the tree stump with a tarp for six to eight weeks to further promote decay.
Remove the tarp or bucket. Use a chainsaw to break the tree down as near to the ground as possible. Once the stump is close to ground level, make slashes into it approximately 1 foot below the ground.
Dig the stump out with the shovel and discard the remaining parts of the decaying tree. Within a couple of weeks of removing the stump, the natural soil nitrogen balance should be restored and ready for replanting.
Place fresh potting soil in the hole. Replant a new seedling of your choice there.