Question
I have a River Birch about 12 feet from the house and 8 feet from a patio.  It is about 15 years old (10 to 12 inches at chest height) and has developed large surface roots (3 to 4 inches in diameter) that are growing under the patio and toward the house.  The one growing toward the house have actually lifted some pavers in a walk adjacent to the house.  I would like to cut five to six of these large roots back to minimize damage.

If I cut these roots back (in the fall) will it kill the tree?  When would be the best time of the year to cut these roots?  

Answer
You can cut the roots back but I would recommend that they be cut as far away from the trunk of the tree as possible along the pavers would be the best. The amount of roots that can be cut is generally a percent of the root area. You can cut up to 20% of the root on a side without causing damage to the tree. Think of the root system area as a pie and as you cut across the pie keep the amount cut off below 20%. I would cut a trench along the patio, and/or house which ever is where the roots are growing, down to 18-24 inches and install a root barrier along the patio. These barrier will keep the roots as they grow back from going under the patio and toward the house.
The fall would be a good time to do this since the tree will have less stress all the tree's energy will be in growing roots rather than leaves.