I have a Formosa tree in my front yard, that I have been trying to kill for the last 10 or 11 years. As you might guess, each time that I cut it down, it comes back with a vengence. In the last year or so, it has come up in a few other areas of the yard (one about 145 feet away from the original plant). It was already a good sized tree when I bought this property, but it was planted nest to the road (In the outlying county). When the highway department mows the edge of the road, they use their boom mounted mower to trim it back away from the road, and this causes new stalks to grow. I need something that will kill the root system and not just the stump(s), or the surrounding plants
If you grind out the stump of a tree it will kill it and the roots. Usually grinders go pretty far into the earth and get most of the large bits. After this is done, the outlaying roots which send up the shoots will die as well, or grind out those too if they have become large.
Some places will rent the grinder but lots of arborists have them as well. If it is on City/County land, call them and describe what you are going through and they might do it for you.
There are stump removal chemicals that can be purchased at the big box stores or a large nursery. My neighbor had the stump of her locust tree ground down and the sprouts still persist to sprout 3 years later.