How to trim/care for shrub/bush

Hey guys, I'm in Phoenix Az and have had this bush in my front yard awhile now: http://imgur.com/a/39Oyj

I don't know what kind of bush it is, sometimes it gets the little purple flowers you can still see some of in the picture.

What's the best way to trim this so it looks less uneven/wild? Under the leaves it seems to be composed of two large branches, in the past trimming too far into the foliage just leaves it looking bare/dead until more leaves grow back.

Is it okay/possible to just cut it down to near the ground, and let it grow back out to start over? Or would this kill the plant? I just want it to look a little more manicured.

Any suggestions are appreciated!