Mulberry trees are heavy water users. They can 'survive' on reduced water but develop stresses that make them vulnerable to a host of diseases such as sooty canker (fungus), slime flux (bacterial), ganoderma (fungus), etc. Your tree's problems may have begun before you purchased the property. Here's a link to information from the University of Arizona.

At this point it would probably be a good idea to start thinking about a replacement tree. Your tree will never regain its strength, but will continue to decline. Fall is a good time to plant and that will give you enough time to choose a tree you like. There are dozens in Landscape Plants for the Arizona Desert which is available on line or as a hard copy from your city's water conservation office.

They are short-lived trees and yours were butchered (branches chopped off to make them bushier) so they are shorter-lived. And they get all kinds of diseases.

Agree with AZtree lover that you need to plan your replacements.

Butchered is right! ["topped"] Ouch! Neighbor's tree looks good form. Seems to be effected by side rubbing up against their roof.

I note both trees appear to have an affected side more than the other sides. What direction does the affected side face on both?

I'd dearly love to have a male mulberry tree like we had at our old property in central Phoenix. But I thought the allergy people got them banned in the Valley?

Most city ordinances prohibit planting male mulberry and fruiting olive due to the huge amounts of pollen they produce. Add that to the fact that they guzzle water and you have trees that aren't compatible with our desert environment.