Trees normally add value to a home but a tree that's in the wrong spot, or is interfering with other parts of the home, can become more of a liability. A tree growing too close to a driveway or sidewalk can easily begin pushing up under the asphalt as the roots expand. The roots can warp or crack the asphalt, requiring expensive repairs. Killing the root immediately when a problem develops keeps the asphalt intact, although it may harm or kill a portion of the tree.
Note where the root or roots are pushing under the asphalt in relation to the tree's location. Roots don't always grow in a straight line from the tree, but that's the general direction to start.
Dig a 12-inch wide trench alongside the asphalt between the root you found in Step 1 and the tree. If the root isn't found, lengthen the trench to either side until you find it. If more than one root is causing a problem, then dig in each location until you've found all the roots.
Dig under the root until it's completely exposed.
Cut and remove at least a-6 inch section of the root with a hand, chain or reciprocating saw. This ensures the root does not reconnect to the tree and will begin to die without support.
Refill the hole, tamp it down, and scatter new grass seed on top.
If the root has left a noticeable bump in the asphalt, wait about a year for the root to decay. On a sunny, hot summer day lay a piece of plywood over the bump, roll over it with a heavy truck and leave it parked on the plywood for several hours.
If the root damage is extensive enough you may lose the entire tree.