This has always worked for me. Save a few plastic cola bottles. I prefer the 12 oz ones. Fill the bottle with water, tie a long string around the bottle neck. Stick the stem into the bottle and use the long tails of the string to tie the stem so it stays in the bottle. Sit the bottle on the ground so it stands up and add a tablespoon of Round Up BRUSH killer to the bottle. Within 2 days you will see the leaves wilt and start to die. The good news is that many blackberry vines are connected by roots to other vines. Round Up goes to the roots and will pass from plant to plant. This is a slow process but you can kill them out of good growing stuff without adversely affecting them. You can do several plants at a time.

Another way to get Roundup on thugs growing among desirable plants is to 1) cut any long stems of the thug back so there aren't any long, floppy pieces, 2) put on plastic gloves,3) put cotton gloves over the plastic ones, 4) pour some Roundup (mixed according to directions) on the cotton gloves, and 5) rub the Roundup on the leaves of the raspberries or whatever, being careful not to get Roundup on the things you don't want to kill. The rubber gloves will protect your hands while the cotton ones will hold enough Roundup to coat the leaves. With a little luck the Roundup will take out the roots of the thug.

Let us know how you decide to tackle the problem and how it turns out. Good luck.