We're in Zone 7B and have grown a wax myrtle hedge along the highway right-of-way for many years. It is a Southeastern native plant that is certainly not fussy as to soil conditions, and it tolerates pruning well. Our wax myrtle is frequently hacked and butchered by the county road crew, and it grows back with gusto. The plants also produce a lot of suckers, which add to the density of the hedge. I think you would have to be extremely skillful at committing horticide to do any real harm to wax myrtle. Of course, I'm sure you could kill it with more than one type of herbicide. I would cut out the dead branch and let nature take its course.

cut it back to the first live bud.. or if none.. to the ground ... just the dead part ..

then sterilize your pruners.. before you do any other cutting on the same type plant ...

who knows what happened to that one branch.. but just in case .... why spread it around

ken