Shoots keep coming up where the tree used to be — what should I do?

A ring of vigorous shoots around the rim of a cut stump, or shoots pushing up through bare lawn several feet away, sometimes in a line that follows a root. The leaves match the tree that was removed. Cut them and they return thicker and more numerous than before. On a still-living tree, the same thing shows up as a thicket at the base of the trunk. The root system is still alive and still holding stored energy, and cutting off the top removed the hormonal signal that kept dormant buds suppressed. The roots are not dying — they are rebuilding a top. That is why repeated mowing or clipping makes the stand denser: you keep removing the shoots without ever touching the reserves producing them. Shoots appearing in lawn away from the stump mean root suckering, which grinding the stump does not stop.