Cutting an exposed root to a tree can be detrimental. A tree has 4 to 7 major roots and if you cut 1 it can be 25 % of it's root structure.
How far out from the tree is the root exposed? If the root is far away from the trunk of the tree cutting it away is an option. The closer into the drip line, the more critical.
Can you cover the root with some top soil?