Prune them off or it will turn into a HUGE bushy thing.

I've gotten mixed messages on mexican elder...is it or is it not a xeric plant? I need a screen that will thrive with little-or-no supplemental water.

Is there anything that can be done so that my Mexican Elder trees won't put out shoots from around the bottom of the trunk? I am constantly having to cut them back, or they just get bushy looking.
Thanks for any advice you can give me.