
This is a sensitive question. An arborist will probably tell you that it is not safe to remove superficial roots. Not only are they necessary to feed trees but they anchor the tree so it doesn't blow down. Oaks have a particular problem, oak wilt disease. No pruning or cutting of roots should take place when leaves are on the tree. This is because the disease that causes oak wilt, a fatal disease, is active in warmer months. Bark is like skin: it protects the tree from infection (and pest infestation). The Univ of Florida has good information that I hope you find useful.
http://hort.ufl.edu/woody/root-prune-guidelines.shtml