Wild blackberry can be a vexing weed almost anywhere in the United States, but it's particularly troublesome in the Northeast, the Southeast, and many areas of the West. The roots are perennial but the canes are biennial: they grow one year, then bloom and fruit the next. Plants spread rapidly by underground runners and by seed.
To control, pull young plants in spring, before they develop a perennial root system. To kill established clumps, repeatedly prune back the stems as they sprout; this eventually exhausts the roots. Or mow the tops and dig out the roots; repeat the process as new canes grow from roots left behind in the soil.
For chemical control, cut stems to the ground and apply glyphosate to the stubs as soon as possible after cutting. Spot-treat any new shoots with glyphosate as they appear. Or spray triclopyr or glyphosate on mature leaves, taking care to avoid contact with desirable plants.