Q.How to get rid of little Locust tree plants that keep popping up all around my yard.
I had a large Locus tree cut down and ever since, these little ones keep popping up all around my yard, in the same places. I keep spraying, they die off and pop up again. Please help.

If you didn't poison the cut stump immediately with a systemic herbicide that kills the entire root system, then the tree has gone into survival mode. The growth popping up in your yard is probably suckers off of the lateral roots that are still alive.
At this point there is no easy way to eradicate the suckers. you have to chase them weekly as they appear and cut or spray them, probably for a couple or three years until they don't come up anymore. Don't let them grow at all or they will photosynthesize and feed the roots.
The only other way is to dig out all the lateral roots.