Trim blackberry canes down to 6 to 8 inches, using garden pruners or loppers. If the canes are long, cut them to manageable lengths.
Insert a sharp shovel into the ground about 5 inches from a clump of canes. Push the shovel deeply into the ground. Lift the cane, along with the root, from the ground. Remove as much root as possible.
Cultivate the ground, using a rototiller. Permanent removal usually requires repeated tillage over several seasons. For small areas, you can use a hoe.
Check the area often. Pull new shoots as soon as they appear.
Cut the canes close to the ground, using pruners or loppers.
Treat freshly cut blackberry canes with a systemic herbicide. Late spring or early autumn treatment is best, as herbicides are most effectively moved through the plants.
Apply herbicides strictly according to the manufacturer's recommendations. Your local cooperative extension office can advise which herbicide is best for your particular situation.
Evaluate the area often. Repeat treatments as necessary until blackberry canes no longer appear.