Dig it out, hire a man with a tree stump grinder and get him to grind it out, or hire the tree stump grinder yourself and get it out. Note that the grinding machines are not easy to use... find a man with a grinding machine via tree surgeons, usually.

We've had several stumps removed by a stump grinder. Google Stump busters (reasonable rates) - you may be lucky and find one in your area. I wouldn't attempt to use a grinder myself, it looks a vicious piece of work and probably works better in a professional's hands.

What kind of tree? Some species will grow back from the roots, and need to be killed with SBK a month or more before grinding.