How short can a cratmertle tree be cut

You mean 'crepe myrtle tree'. And here is the info for trimming:

To develop a tree shape, remove all limbs growing from ground level except the three to five strongest limbs. As the tree matures, remove lower, lateral branches (“limbing up”) one-third to halfway up the height of the plant. Remove branches that are crossing or rubbing against each other and shoots growing into the center of the canopy. Make your cuts to a side branch or close to the trunk. Head back wayward and unbranched limbs. As it grows taller, remove lower branches as needed. Remove any future growth from the ground to retain the desired tree shape. This basal sprouting may occur whether the tree is being pruned or not. Pull these out when succulent instead of pruning them.