It probably would kill it at that spot but I think they can spread from root runners. I am seeing a lot of sprouts around some of mine. Either it is that or seed sprouts. Not 100% sure. I would just spray the sprouts too if you get them.
Those are stump sprouts. Perfectly natural for a Crepe Myrtle to sprout these.
Glysophate (Roundup) is a systemic herbicide. Put it on the cut off stump and it will kill the tree and any of its stump sprouts.
