It's a normal feature of Crapemyrtle to have sucker growth (the shoots arising from the roots or trunk base) as they mature, though trees that are stressed or pruned too heavily can sucker much more abundantly. Suckers are best removed manually by clipping them off as close to the soil line as you can get without wounding any nearby trunk bark. There are very few chemicals used to treat suckers to discourage their regrowth (arborists might have access to them, and they may need one or more annual reapplications for the life of the tree), since all other types of herbicide will either not work well for long (if they only kill foliage) or will cause damage to more of the tree (if they are absorbed into foliage and moved into roots).

Miri