Mowing over the suckers , or digging the suckers out are non-toxic methods of removing the suckers. If the stump is not ground down or removed, the suckers are most likely coming from the root stock. It may depend from where the shoots are coming. Most fruit trees are grafted on root stock. Even if it is an ornamental/flowering plum and not a fruiting tree, it was probably a graft. If the suckers are coming from the base circling the trunk, it's likely from the root stock and not from the graft. It's unlikely you will get any tasty fruit from the root stock, but you could get flowers. If there is any amount of trunk and it's sprouting from there, you could try thinning out the suckers so you have four or five actively growing and re-establishing the tree. You may be better off starting over, by grinding the stump (that will kill it) and then adding nitrogen to help break down the sawdust and roots. You need to leave it for a couple of years before replanting.