Almost impossible to get rid of, you have to dig it up, poison the ground, burn it, then scatter the ashes at sea, and that's no guarantee. A nuke might not do it, either; probably be the first plant to come back. Blackberries, kudzu, English Ivy, Morning Glory, most of those grow in my yard and fight for domination. Hard to tell who is winning.
Um. The blackberry's redeeming factor is the fruit. It tastes good, has vitamin C, and while it's spendy if you buy the organic version at New Seasons Market, five or six bucks a pint, something like that, you can pick the organic variety any place you can find it, at the cost of a few thorns and stained fingertips. In twenty minutes today, my wife and I picked six pints–along with half a gallon of Japanese plums–at a local park a stone's throw from our house.
The dogs will forage for the berries closest to the ground, and Jude will eat them right off the canes. Eats the plums, too, and spits out the seeds.
If we pick a bunch of berries and plums over the next couple weeks, we can freeze them, and use them for pies, jam, or even booze. My wife makes a dinner liquor with vodka, brandy, lemon juice, sugar and blackberries you age in a dark closet that will knock your socks off. She also makes a Japanese plum pepper jelly that adds a nice taste to all kinds of dishes.
Come mid-winter, blackberry cobbler or pie is a nice treat, and all it takes is a few minutes in the sunshine whilst walking the dogs.