If you’re removing Himalayan blackberries you have to dig the rhizome out. It’s not enough to cut it down. Basically you take an adze or similar and cut in where the shoots are coming out of the ground. Then pull up on the shoots and a little ball will come up with them.

Here in Washington State the Himalayan blackberries are an invasive species which grows all over the place. There are no natural predators here. If they become established then they kill everything around them including some trees. The only reliable way to remove them is by digging out the rhizome after cutting them to the ground. It can take several years to completely eliminate them from an area