Will cutting one root hurt this tree?

Your tree is fairly large so it will have a root system extensive enough to sustain the tree if you only cut the ONE root. When you cut the root back, cut it cleanly to help guard against the development of disease.

The root system of semi or fully mature trees generally reaches far beyond the plant's dripline. When roots grow near or above the soil surface it is usually caused by one or more of the following:

• Shallow, frequent watering
• High water table
• Hard soil layer (hardpan) just beneath the surface.

It may be helpful to examine your tree's location to see if any of these conditions exist.