When you cut the suckers, paint the bark at the cut with Bonide Stump and Vine Killer. This will get transmitted to the roots and kill them. This would have been ore effective had it been done when you cut down the parent tree. It may continue to send up shoots after your initial application but, if you keep cutting and painting the bark with the herbicide, the tree and its roots will eventually die off. Always read and follow the direction on the package.