Answer: You should be able to kill the tree and its roots by using a vegetation killer called Round-Up. The process is simple and you don't need very much (perhaps a neighbor already has some?). All you need to do is cut the main stem or trunk of the tree and then paint full strength Round-Up on the cut stump. The chemical will travel down to the roots and should kill the roots within a few days.
Best wishes with your garden!
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