Cut around the tree's root system deeply, using a spade, deep enough to accommodate the plant's root system. Use the spade to cut underneath the stump of the tree to remove a large extent of the roots. Roots will be more extensive in sandy soils and somewhat constricted in harder, clay soil. If your snowball bush is large and tree-like, an axe or chainsaw may make this process easier.
Apply herbicide to freshly cut stump, focusing on where the bark joins the wood of the stump, as well as on any exposed tree roots. Use a brush to ensure complete coverage. It may be beneficial to cut the root before application to improve absorption, such as by drilling several holes or splitting it with a wedge. Chemicals should be applied within 24 hours of cutting down the plant.
Cut off any sprouts that emerge from remaining roots, or spray with an herbicide containing glyphosate. Monitor the plant and remove sprouts continuously to maintain control.