Can I cut the roots of a neighbor's tree that are encroaching on my lawn and possibly damaging the house foundation?

The tree is quite large and was planted approximately 2 feet from the house boundary. The roots are now large and, since the ground is largely clay, the roots snake along the surface towards our garage. I broke a mower blade a couple of years ago on the roots. The current owner didn't plant the tree and has stated he can't afford to pay to have the tree removed. I don't know what my options are: cut the roots (which may kill the tree)? , check for garage damage and sue him to pay? He's not a bad neighbor, but I think he just wants the problem to go away. Thanks for any advice.