Maples are known for their tendency to surface root. They do this for various reasons, including soil compaction, but once the tree has large roots on the surface, you are right to be concerned. Cutting the roots may harm the trees. One suggestion is to use a very light coat of mulch (1-2" max) in a large ring around the tree instead of grass. Grass has a hard time competing with tree roots, and at this point you need to decide which is your priority: the grass, or the trees. They don't do well together; what is good for one is not good for the other, and vice versa. I have attached a publication that deals with this exact challenge. Please let me know if you have further questions.