This is not precisely applicable to removing stumps already cut low, but I have removed about ten large oak trees that were in locations that were problems - locations threatened structures or other issues (oak trees are notorious for falling over or having large branches break off). I needed the stumps also gone. After taking out the first stump and leaving a hole the size of a small car after days of work, I learned to leave about 8 feet or so of trunk - then I could dig around the base and cut as many roots as possible and then with logging chains had enough leverage so that I could pull and rock the tree from several directions until it gave way. Not easy, and not an option for stumps already cut down low, but it worked for me. These were trees in the 1.5 to 2' +diameter range, with the largest 67 feet high. I am really glad, though, that I don't have any more to take out.
For other locations, where I did not need to have the stump out right away, I used the chemical route - drilled a lot of holes and kept adding the stuff. It is, as stated, a very slow process but will eventually work.