I use a combination of digging, spraying (gasp!) and goats depending on the location and terrain. Tools for the job, etc.
The tools for this job were my goats. But as you might recall, they weren't greeted with applause from all corners upon their arrival. People seem to think goats are trouble, what with their insatiable appetites for shirty-irty-irty-irty-irts on liney-iney-iney-iney-ines, and tendency to butt anything they get near.
These ideas are fallacies, especially with goats so young; goats I'm training to the tether; goats that respond well to kind conversation and a friendly pat.
I put them onto a blackberry infestation for a week. Before photos on the left; after on the right.
As you can see, the goats are pretty effective.
The best thing about this is that this spot is a mess, contour-wise. You could brush-cut, but not mow, and the blackberries do tend to wrap themselves around the brushcutter head with a vengeance. As it was, they tore my dress while I was moving the goat house. And my knee.
Oh, another bonus? They did it while I was at work ... and in the hammock.