I've heard of guys using a single-shank subsoiler and using it to run a tight circle around the stump to break as many roots as possible. Not tried it myself, so can't say how well it works. It does make sense though, for many trees, but you'll have troubles with oak (or similar trees) which have a long taproot in the center. After cutting as many roots as possible, pop it out with your loader, or hook on a chain.
This isn't as effective as a backhoe, but it's a whole lot cheaper.
John Mc