Certified GKH Gardening Expert
You will have to keep all new growth cut as often as possible. Pour boiling water on all parts of the plant and the area surrounding it. This will usually do most of the work. If these manual methods don't work, you will have to turn to chemical herbicides, such as a brush killer.
This article will help: https://www.gardeningknowhow.com/edible/fruits/blackberries/invasive-blackberry-control.htm