Question
Hi...
 
 I live midway between San Antonio & Austin just NE of IH-10 and Hiway 123.
 I have what we call a "Black Bush" that has been growing under my fenceline for 30 years.  It has Wicked 2 to 3 Inch Hard-As-Nails Thorns.
 When I first moved here, I cut the thing below ground level; but it came back.  The next year, I cut if off below ground level, and place an upside-down coffee can over the stump, then covered it all up with dirt; but again, it came back.  The following year, I again cut it, put salt and oil around the stump, and another coffee can, and the doggone thing continues to come back up.  
 How can I get rid of this thing once and for all ???  I'm DESPERATE !  
 After all these years, it's more a nuisance due to all the flats it gives my lawn mower; but I just don't like the idea of the damned thing winning !!!

Answer
I would use a herbicide on the sprouts and this will kill the root systems.Here are a couple of choices to use. I would try the Roundup first.

A 1.5-2% solution of glyphosate (2-2.6 oz of Roundup/gallon water) applied as a spray to the foliage of seedlings will effectively eradicate honey locust. Roundup should be applied carefully by hand sprayer, and spray coverage should be uniform and complete. Do not spray so heavily that herbicide drips off the target species. Roundup is a non-selective herbicide and will kill any plant it comes in contact with. Glyphosate should be applied while backing awayfrom the treated area to avoid walking through the wet herbicide.

Chemical Controls
Grazon P+D: High-volume foliar treatment of individual plants
Apply 1 gallon Grazon P+D and 1 to 2 quarts surfactant per 100 gallons of spray mix. Spray to thoroughly wet foliage in the spring when leaves are fully expanded and mature

Remedy: High-volume foliar treatment of individual plants
Ground application of 1 to 2 quarts Remedy alone or in combination with 2 pounds 2,4-D per 100 gallons of spray mix. Apply sufficient spray volume to thoroughly wet all leaves, stems and root collars after the rapid growth period of early spring when leaf tissue is fully expanded and terminal growth has slowed. Brush regrowth should be at least 4 feet tall prior to treatment to ensure adequate foliage for herbicide absorption.