Crape myrtle suckers are persistent but it's not impossible to get rid of them although it will take time.

You can apply herbicide labeled for control of "broadleaf" weeds or a non-selective herbicide that will kill all vegetation to which it's applied. Check with your local nursery and read the labels carefully before purchasing, as these products can damage desirable plants if applied improperly.

Products containing 2,4-D can be absorbed by the roots of other desirable plants. Products that contain glyphosate can't be absorbed by the soil but can harm other plants if applied on a windy day. You should also consider how long a product will remain in the soil if you plant to replant where the chemical will be applied.

A single application will probably not be sufficient. The root system has a lot of stored food reserves that may be used to continue producing new sprouts. The chemical you choose will kill the new sprouts, but others will form. Over time, you can deplete the food reserves and the sprouts will stop forming.

Should you decide against chemicals, a mechanical method for removing the sprouts is to dig up or mow them. Digging a few inches below ground level will be sufficient and better than just mowing. In either case, whether you use mechanical or chemical removal, the object is to deplete the store food reserves in the root system by removing new growth after it draws on the stored food but before it begins to return food to the roots.

Please let us know if you have additional questions.