You could do the opposite of all the suggestions for caring for a healthy tree. None of these will kill the tree instantaneously, but they will all take a few years off the tree's life.
For example, prune a few branches without making an undercut. Let the branch rip a long strand of bark off the tree.
Prune too close to the main stem, to introduce rot into the trunk.
Install a sidewalk under the tree, that cuts through the top 12 inches of soil and kills all the roots there.
Run the lawnmower right up under the tree, where it will damage the bark at the trunk.
Mulch around the tree, but bring the mulch all the way up so it rests on the base of the trunk. If you can get a root growing in this mulch, that root can act as a girdle.
Smother the roots by re-landscaping around the tree, covering most of the roots up with at least 12 inches of soil.
Anything you can do to force the tree to put out leaves multiple times in one year will deplete its stored energy. Getting something to graze the tree in spring right after the leaves bud out will weaken the tree.