Examine the tree and locate all the suckers.
Cut the sucker as close to the base as possible with a pair of sharp pruning shears or a machete. Dig into the soil with a small shovel to expose the base of the sucker, if necessary.
Treat the exposed root base of the sucker with triclopyr or glyphosate, herbicides that will inhibit the sucker's future growth. Use a thin layer of either herbicide to prevent poisoning the rest of the tree.
Continue to monitor the tree for any new sucker growth. Treat these suckers in the same fashion to prevent them from growing, and potentially damaging any surrounding cement or asphalt.