They make a chemical that deteriorates a stump. It has some stupid name like 'Stump-B-Gone' or something like that. You drill holes into the stump, pour in the powder and then add water. Its not instantaneous though. I used it on an old stump in my back yard and after a year I could basically pick the stump out with a shovel.
Not sure Id want to use it in a food plot for animals though... can you burn them out?