I, too, would call that crapemurder. Pruning that way makes the tree push out an overabundance thin, weak growth that pronounces the unnatural look of the hacked back limbs. There's nothing less natural looking than a 1 cm wide stem coming out of a 3 inch thick branch. Unfortunately the look is not only ugly it is not healthy for the plant. The new growth of a crapemurdered tree tends to be very prone to powdery mildew and storm damage.
So how did this practice begin in the first place if it's such a bad thing? In the colder states, crapemyrtles die back quite a bit during winter and they have to be cut way back just to remove the dead parts of the branches. As northerns began moving south they brought the practice with them and over time, people adopted it as the proper way to prune. But, in warmer regions the only pruning that is necessary is just enough to remove last years seed pods, any dead branch tips and crossing limbs.
As for the Euonymus at the base of the tree (pardon me if someone has already suggested this) I would "paint" the leaves of it with Roundup or a similar herbicide. The leaves will draw the chemical into the roots of the Euonymus and kill it without affecting the crapemyrtle.
