Cheryl, did your suckers break off cleanly from the root that spawned them, ending in a whitish tip that has no roots of its' own? That's what's happened on the ones I haven't wanted to dig (and disturb plants I've put in the removed-grass area.)
It's said that the general rule for woody entities is that roots spread approximately the same distance from and under the trunk, as the trees' height. A 10 ft. tall tree should have roots that extend out and down about 10 ft. So if it's a type that can make suckers, they could show up anywhere within about 10 ft of a 10 ft tall tree. IDK how CM compares to this kind of average.