Or incorporate the stump into your garden design as a pedestal ... Don't be tempted by the chemical cocktails “guaranteed” to kill a tree that you may find on the internet.

Pour 3 to 4 ounces of tree stump removal chemicals into each of the holes in granule form, then fill the holes with water so ...

"This would probably be illegal and might well kill whatever was living on the rotting tree stump, though. It's better to have decomposing wood in a garden. If you have a dying tree, let it die.