You can spray mesquite with chemicals dozens of times and still not kill them all. but at the same time what you are doing is introducing chemicals into your soil that takes years for it to recover properly. Large mesquite trees are easier to get rid of than the off shoots from the roots which can be as much as 40 feet from a parent tree. I decided to make a root plow to assist in ridding mine and a friend's field of some of the many smaller mesquites for one he made the mistake of spraying his field with remedy mixed with diesel as per directions but then he didn't go back and spray a 2nd or 3rd time. He also mowed them down after killing them but didn't mow regularly enough to keep them from restarting. Just like some weeds if you mow frequently enough eventually you can kill it off.
Another way is to plow the roots out of the ground. A good way to do this is with a multi shank heavy duty chisel plow. But you need to Criss cross the field several times to break up or cut up the runner roots and to bring them to the surface if you can tear them up enough and often enough they will not re generate. But the whole field is tilled this away if you have native grasses already and you don't want to have to re seed several acres. You use something like this for spotty infestations.
Made entirely out of scrap that was already loaded to be hauled off but hasn't been because the trailer is not full.
Here are some examples of what came out of the ground the thin stalks were the only thing above ground all of the black part was what was dug up