I have a 10 yr old parkway tree which measures around 20" circumference. I have multiple horizontal tree roots that run simi-exposed along the grass surface and are killing the grass in these areas. The roots extend 10 to 20 ft and average 6 to 8" in diameter.
Can I remove some/all without damaging the tree?

Yes, so long as you don't do too many at once. You'll probably have to take a hatchet to sever the roots if they are that thick. Just don't do all at once and your tree will be okay.