I second Steph Hen's advice about pulling suckers, rather than cutting them - obviously one needs to pull them as soon as they are discovered to stand much chance of ripping them off the root manually! (I have yet to test whether it is possible to rip larger suckers from the root with the help of a tightly bound, low-tied strap and self-propelled garden machinery or a tractor.)
I started looking into this issue recently because one of my clients has a number of root-suckering trees (lime, sumach, foxglove tree). I have yet to accumulate any great knowledge on the matter, but pulling is definitely a recommended option. I can also advise, from personal experience, that cutting the offending root tree-side of the sucker can result in more suckers from the tree-side end of the severed root!