Q.continually “bleeding” mesquite after branch cut
Several years ago a large branch of an old mesquite in our AZ yard snapped in heavy wind and had to be cut off totally. Since then the “wound” has continued to “bleed”, and since that part of the mesquite overhangs a flagstone terrace, the terrace continues to accumulate sticky black pitch. After rains, this splatters even farther. How can the “bleeding” be stopped? How can the accumulation of pitch be cleaned off the flagstone?

Certified GKH Gardening Expert
It sounds like the tree has slime flux. The jury is out on this disease in terms of how lethal it is. Some people feel that Mesquite can recover from it fine after being infected while others feel that it is potentially dangerous to the long term health of the tree.
There is no known "cure" for slime flux. It is something the tree has to battle itself. But, proper water and nutrients will go a long way to helping it recover.
As for cleaning the sap, this article may help:
https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-remove-tree-sap.htm