Most of a tree's root system extends as far as three feet into the ground. Roots anchor the tree into the ground and absorb water and nutrients for food. If damage is done to any part of the roots of the tree, it can cause parts of the tree to die or thin out. It is much like the nerve system in a human. Each root is tapped into certain parts of the tree.
Determine the diameter of the tree in inches. You can do this by wrapping a tape measure around the bottom of the trunk of the tree. Multiply this number by 1.5. You can not cut any roots that are within this many inches of the tree trunk or you will run the risk of damaging the tree. Simply use your tape measure and measure out from the bottom of the tree.
Use a shovel to dig in the area outside of the distance from the tree that is safe. These are the only roots that can be trimmed back. Dig down until you find the roots. Taproots can be very deep in the soil, so if you want to remove all of them you may need a backhoe.
Cut back the roots during June and July. This is the period of growth for most trees. Cutting tree roots when the tree is dormant can kill the tree because the tree is inactive and will not put out any new roots.
Trim down a few inches off only the smaller roots and not the larger, main roots, by using a chainsaw or hacksaw. Doing this will offer the smallest risk of destroying the tree. The only time you should remove any roots is when they are destroying concrete, driveways or foundation. If you decide to cut the roots, be prepared to deal with greater problems in the tree, and even its death.