Answer: If your plum tree is struggling, the roots may be putting out an abundance of suckers, knowing that the top is stressed and may die. There's no way to stop the suckers from forming, but you can routinely cut them off at surface level, or dig down to where they attach at the roots and pull them off. If you pull them, they won't resprout (but others may form). If you cut them down, they'll resprout. Sucker production may slow down once the top of the tree is heathier. Water deeply once or twice each week, and prune your tree back a bit to encourage healthy new growth.
Best wishes with your landscape!
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