There's another approach which is easy, inexpensive, and won't damage
anything, but it does take a lot of time: rotting it out.
Wood will decompose into soil given four additional ingredients: air,
water, nitrogen, and bacteria.
Air: Expose as much of the stump as possible. Drill holes into it to
let air in.
Water: Water it frequently; try to keep it moist. If you can, rig up
a drip to keep it constantly moist. If possible, keep it out of the
sun so it won't dry out as quickly.
Nitrogen: Apply a high nitrogen fertilizer
Bacteria: Get some rotten leaves or soil (the stuff you scoop out of
your gutters is good), and spread it over the stump.
If you see mushrooms growing on and around the stump, and see grubs
burrowing in it, then you are doing it right. Fungi, insects, and
bacteria will all work to convert the wood back to soil.
If you keep a compost pile, start a new one on top of the stump.
It may take a year or more.