The looming question is what killed the tree in the first place? Borers? If 'yes', and you want a new clump, you should have an immediate plan to deal with whatever killed the tree.
If you want to kill the stump and epicormic sprouts, there is a product called Tordon RTU (ready to use). Simply prune sprouts off near the bade and paint the cut with the product. It's very effective.
You can also starve the plant by removing any new growth immediately, before it has the opportunity to contribute meaningfully to the tree's food supply (sugar made during photosynthesis).
If you can deal with the original cause of the tree's demise, you can surely start a new clump from the shoots. That's usually best done by cutting the stump back almost flush with the soil line and choosing sprouts that originate close to the ground.
Image of a maple taking it's first step toward a clump/grove style bonsai - same principle/concept.
Al
