Until the roots are gone the plant will keep re-growing. So the best method is to use a weed killer that the plant will translocate down to the roots. Weed killers with 2, 4-D in the active ingredient are the most efficient for this purpose. Purchase the ones labeled to control woody weeds and with a high percentage of the active ingredient.   Read and follow the directions carefully, This weed killer can not distinguish between a weed and a cultivated plant. Do not apply with spray on a windy day.   I suggest you cut back the crepe myrtles. Allow to grow about three leaves then use a paint brush or paint sponge to apply the weed killer on the new tender leaves. The weed killer is an acid so you will see the leaves burn quickly. Do this with all new growth until there is no more. The weed killer taken down to the roots will help the roots die sooner than just cutting down the the suckers.   What you are doing is denying the plant photosynthesis so the roots will not be replenished. You can accomplish the same with continually mowing or string trimming. This will take longer.