Question
I live in Albuquerque, and did not water the tree enough (strict water restrictions) can I grind the roots to ground level without killing the tree? It's approx.12 years old, and 25 feet tall with grass all around, making it very difficult to mow the lawn.

Answer
Sounds like the wrong tree in the wrong place.  Consider replacing it with something better behaved (Ash, Chinese Pistache, or Chinese Elm)

http://aces.nmsu.edu/pes/lowwaterplants/large-deciduous-trees.html  

Under-watering the tree did not cause this problem.  The shallow roots are an important part of the tree's health, and you can try to "grind" them, but you'll now give pathogens and diseases a new path in to the tree's system.  No guarantees that it will "kill" the tree, but it won't be good for its health.

I have one in my backyard, and we only grow kids under it...bare dirt, sandbox, and a swing.  Ours is about 20 years old and in really poor health; but thats another tale.

So sorry.  ~Marc