We just planted a small mesquite and my dogs chewed the entire top of the tree off. Is there any chance this tree will grow back? Could I salvage the top by propogating some of the top branches?

Odds are low.

If you had acted really fast, you might have been able to stick part of the top on to the bottom and have it grow back together (look up splice grafting - smooth clean cuts and a similar diameter are key)

A day or two later when things are starting to dry up it probably won't be successful (you might not have been anyway) but it doesn't hurt to give it a shot.

Don't give up on the stub still in the ground, the mesquite might grow back from the roots.