In answer to your question , you can cut large roots from a tree in cases like this often without damaging the tree. Yes roots , especially on an elm can cause foundation and sewer problems.
On the otehr hand I have seen trees perish by cutting to much and have also seen trees capsize over from having to many roots cut on one side that anchor the tree in.
I always recommend on a large mature tree to involve the services of a trained Arborist so that they can inspect the health of the tree and give you recommendations on how much to trim and ny other maintenance issues they see while examining your tree!!

Steve, I agree.  We're trying to proceed minimally just because of that concern.  Thus, we've determined only this 1 anchor root is an issue.
So, in your opinion, you don't see an issue with cutting this 1 area?  Are Elm's sensitive to even 1 anchor root being cut?  If all is okay, would you recommend using a pruning sealer to keep bugs from getting into the cut area?  Thanks again! :)

Again in theory it should be ok, I still always recommend consulting a good Arborist as i cannot see and inspect the rest of the tree or any other things that might be a problem. If I was going to do it i would carefully excavate around the root so I could make a good clean cut and then seal it immediately with a pruning paint to help protect it from bugs. 
elms are not any more sensitive to trimming the roots then any other tree in same health condition. Hope that helps?

Steve, that definitely helps!  Thanks so much for all the input!

Your very welcome, please feel free to call the office if you have any otehr questions.