We have lots of wild blackberries here as well- what I do is either in the fall or very early spring, I'll do some aggressive thinning of every cane that fruited the previous year. It should be relatively easy to see where the fruit was; the spent fruit clusters/stems should still be visible with everything bare. I also cut out anything that's headed for the trees; I don't do it for the berry aspect but because the plants are considered a noxious weed here in WA. You can either cut them back to the ground or just go in to a node, it's up to you and depends on what kind of control you need. I usually leave a foot or two, myself- I don't want to encourage any more growth from the roots than I have to.
