Any plant if cut often enough will give up the ghost. The question is how often is enough? It seems to vary from plant to plant. I am not sure about buckthorn but your suggestion sounds better than doing nothing. For multiflora rose, I noticed it has to be cut several times a year to have a chance of killing it off this way and even that may take years but I have done this successfully. Ditto for porcelain berry. You could try a well-timed application of herbicide on your buckthorns to speed things up. See the discussion on this forum about 100,000 buckthorns to kill. Well-timed cutting might help you to at least diminish seed production.
May the force be with you.

In my opinion you'd have to cut the buckthorn every month, possibly every week for a more than one growing season to be effective. I'm still not sure it would even kill them outright. I have buckthorns that have been growing for years in my lawn getting cut every few weeks.
I find that painting the cut stems with a triclopyr based herbicide in fall is the easiest way to kill buckthorn. I have had close to 100 percent kill rate with this method.
If you do decide to go ahead with the brush hogging method, I would advise doing it when the soil is frozen. Brush hogging when the soil is thawed can disturb the soil, aiding the spread of garlic mustard.

We are in a battle with multiflora rose and privet. These are very invasive and will resprout if simply cut. We spray the newly cut stump with Tordon. This works! If not for Tordon, I would just give up.

My mistake. The discussion about "100,000 buckthorns to kill" was in the natives forum.

I'm battling the multiflora and thinking about caving in and buying the overpriced Weed Wrench. Such a handy tool...at such a non-handy price! But it would clear out multiflora without chemicals or repeated cuttings (and more repeated cuttings....and more...).

Here is a link that might be useful: Weed Wrench Site

I have a Weed Wrench. It works well. When I called to order mine I actually spoke with the inventor/owner who struck me as a very nice guy.

I have a lot of Buckthorn in the back of my lot. I've cut and applied herbicide to almost all of the mature shrubs, and pulled or Weed wrenched many of the smaller ones. There are lots of seedlings out there left though and the seed bank must be impressive too. I will probably do a combination of mowing (along the path) and pulling for the remaining plants. Not sure how frequent the mowing would need to be though. It's an ongoing experiment to find the easiest ways to get rid of these invasive plants!

As for the Weed Wrench, it was well worth the money and I could have used it years ago. I have dug out so many invasive shrubs and small trees in this yard with a shovel and had many more to go. (Also have lots of Honeysuckle, Burning Bush, Barberry, Rosa multiflora, Norway maples). The Weed Wrench sounded like it would make the job easier and quicker, and it does. I bought the medium sized Weed Wrench, which is the 2nd largest and weighs 17 pounds, sells for about $150.

Your lot sounds like mine. We cut down scads of buck thorn and now we are working on the invasive with the black berries. I cannot remember the name right now. It is a non-stop fight and not a lot of fun. I am curious to hear if you think your burning released any seeds that were dormant? I have been debating burning the ground in my woods to see what I could get to grow.

OK, OK...I'm going to purchase the weed wrench! All rave reviews across Gardenweb, and I'm sure I'll never regret the price. Plus, a small company has to make money, I know...I'll consider it an investment! =)

Be careful where you use that Tordon! Remember, all those tree & shrub roots are somewhat intertwined. We sprayed a small patch of buckthorn that was growing in a grove of Kentucky Coffee trees and killed a few of our trees. Made us very sad. Now we don't use Tordon near any trees.

Another vote for the weed wrench! I have a suburban lot here in the Twin Cities that was seriously neglected by the previous owners and I've removed a fair amount of buckthorn. Fortunately it's almost all small enough to be handled by the medium sized weed wrench, well worth the money. I'm in the process of replacing the buckthorn with natives (serviceberry, etc.) I've counted/photographed 60 yard bird species and hoping to get more!

Check out my backyard bird photos and live feedercam.