Grind out the stump and any visible roots to at least 12 inches below the soil with a stump grinder. Grinders can be rented from equipment rental companies. Another option includes hiring a stump removal service company to do this for you.
Drill holes into the soil and any remaining root or trunk sections in the ground using a drill.
Apply a nitrogen fertilizer, following the label directions for mixing and application rates. You also can apply organic mulch. The application of nitrogen or mulch will encourage fungus to grow, which will accelerate the decay process of the remaining roots.
Pile moist soil over the fertilized area in a mound. Repeat applications may be necessary to ensure all roots have decayed and died off.
Make several cuts around the circumference of the stump using an ax or a hatchet.
Apply herbicide into the wood inside the fresh cuts and allow it to absorbed into the stump.
Repeat treatments if you see new growth. Several treatments may be necessary to kill all remaining roots and new growth.
Apply herbicides such as bromacil, hexazinone and tebuthiuron directly to the soil around the stump, following the label instructions for soil application. The herbicide will travel with rainfall into the roots of the stumps.
Treat multiple stumps in one area by applying concentrated solutions of hexazinone or tebuthiuron-based herbicides in thin bands around the circumference of the stumps, spacing each band about 2 to 4 feet apart.
Repeat herbicide applications if new growth is seen.