kill stumps
65% diesel, 10% Cide-Kick, 25% Remedy.
Diesel will evetually break down, Cide-Kick is a commercial penetrant, Remedy is a woody plant Herbicide. In Texas it is used and labelled as brush control and no license is required to purchase it. Your state may be different.
As soon as possible after cutting stumps, so they do not "seal" themselves. If it has been some time skim the stump top with a chain saw to open a new wound and wet the surface and if it is a legume type like mesquite or a sprouter like red berry juniper or huisache, wet it enough that the mixture runs down the side of the stump on all sides to ground level - 90%+ won't come back from the stump with this treatment.
Be careful of the depth of the water table and adjust amount of mixture accordingly. Here, we dont have a lage concern, for the watertable is several 100 feet deeep and many strata to pass through, thereby the active ingredients are broken down well before they pose any threat. Besides from personal experience, you can literally bathe in the stuff an not be and suffer nonononono illlll effffeccctssss.
I do agree with Husky however, if you are looking for drawing in ruminant animals (deer, moose, etc.) the young regrowth is invaluable for providing browse - shred it every 4 years or so and let it grow tender leaves for them. Eventually the stumps will die on their own in most cases if you periodically shred the top growth at certain times of the year, but in the meantime you provide good browse for the wildlife.