Dead elm trees may pose a threat to surrounding elm trees as the dead wood becomes a breeding ground for the elm bark beetle and Dutch elm disease fungus, according to the University of Minnesota Extension. Remove an elm tree quickly and properly, taking special care to dispose of all parts of the tree.
Cut large limbs from the elm tree by cutting them at their base with a chainsaw. Use a ladder to reach higher limbs. Keep children and pets out of the way to protect them from falling limbs.
Cut down the elm tree's trunk with a chain saw. Make a V-shaped cut on the side in which you want to have the tree fall. Make another straight cut on the opposite side about 2 inches above where the V on the first cut intersects. Make each cut about one-fourth of the trunk's diameter and keep the remaining piece of wood in the middle for the trunk to hinge upon.
Shut off the chain saw and start to head away from the elm tree as it starts to fall.
Break up the elm tree's stump with an axe until the stump and its roots start to easily lift out of the ground.
Drill a few 1-inch deep holes, spaced evenly around the perimeter of the stump, if you cannot remove the stump with the axe. Pour a stump removal chemical into the holes and let it sit until the stump takes on a spongy consistency. This can take months or years. Break up the stump with the axe.