Mock pear roots sprouting leaves everywhere?

We have a mock pear tree in our yard and its roots are sprouting what looks like little trees all over around it. My question is how on earth do I get rid of them? They are horrible! I keep cutting them down and in no time they grow right back up. I would try spraying them with something but I'm afraid of killing my tree in the process. I currently have about a 6 foot ring of mulch around the trunk. Thats about 8 to 10 inches deep. Which, by the way, they even sprout up through that!