Elderberry or Sambucus is a native plant and very persistent. The best method is to make a clean cut of the stump then immediately paint the cut with Roundup so that the poison goes down to the roots and kills the entire plant. You can also try cutting the plant to the ground then covering the stump with a bucket so it gets no sunlight. It will still sprout but the new growth will be weak and you can keep cutting it off then recovering with the bucket to block light. Eventually the plant will exhaust itself and give up.  I regret saying "Keep Growing" as my sign off to you, but I think you will be able to control the Elderberry and you and your garden can Keep Growing, Marianne Binetti