Read my lips: Cut it off at ground level, any way you wish to do so, and you will turn a single stem into multiple stems that sprangle out over the entire area.
If you have been in the Victoria area, then you know that much, much of that country was root plowed in the 50's thru 70's.... and you see how it is now, again, thick in mesquite... sometimes one stem per square foot....If it were cheap or realistic or possible to achieve control, the people in that area would have done so. This is the heart of where the cattle industry in the US was born. The Longhorns came from there for the long cattle drives. The land is very productive when grass can grow there... mesquite sucks all the moisture from the ground and all good grasses are uable to grow in its canopy.
Constant, continuous, annual attention to the entire area, for 15 plus years is the ONLY way to eradicate it and regain grassland. Researchers planted a bunch of mesquite beans in a pot with steralized soil. Provided with moisture, warmth, etc. they began to sprout. They removed and counted every sprout as it came up... 15 YEARS LATER THEY WERE STILL SPROUTING. Point is, the seeds can lie dormant for years and years, so even after all visible plants are removed, new ones keep arising.
Mechanical control alone will NOT do it.... the root buds string out along the roots....for quite some space... unless you remove ALL roots from the ground, even if you remove the upper part of the tree and MUCH of the roots, there will still be root stubs from which new plants will appear next year... or even the same year...leave them alone for a while and your infestation returns worse than ever... so, you MUST come back, again and again and remove EVERY offending plant, one by one...using some method...mechanical (in the old days, we had wetbacks who grubbed by hand) or chemical.
Note that Texas A&M has spent years and years seeking solutions. What you read now is the result of over 50 years of efforts and studies:
Brush Busters Brush Control Program
You will note, reading the above, that they have abandoned the mechanical "control" methods in their recommendations. Thus, abandon ideas of a " new machine."
Clap your hands..... and believe
Ddivinia, SORRY for perhaps the most egregious thread hijack I've ever done.... this should be in a thread regarding brush control... this will be my last post re mesquite brush in this thread. There is nothing more to add.