Maybe a good idea to mention that the id suggested was Rubus armeniacus, Himalayan Blakcberry, an invasive in California. You said in your other post that it couldn't spread because it is hemmed in by walls. But birds and other wildlife eating the fruit can spread it far and wide. It might be a better idea to get rid of this plant and obtain a good cultivar of blackberry suitable for garden culture in your region. Here is a link that might be useful: R armeniacus

Thanks! The color of the canes did catch my attention, and while I'm not a big eater of fruits, I should make more of an effort to do so. Problem is, the birds around here know better then I when something ripens, and by the time I find out it's ripe, it's pretty much all gone! I guess that's the thanks I get for keeping their feeders stocked and their bath full, LOL. If the rain holds off, I may get them tomorrow. vince

The further down you probe and cut out, the longer it will take for them to re-appear. Perhaps you can estimate a straight line from original to runner sprout and chop off the root of the runner on the inside of your original raised bed. That would remove some energy but would not prevent the remainder of the runner from re-sprouting unless you can fish it out of the ground from beneath two raised bed sides. Usually repeatedly removing sprouts at ground level makes this activity go away by mid summer, and of course it returns next spring.

Fuel oil isn't necessary. Paint the newly-cut stumps with glyphosate (Roundup) or triclopyr (Brush B Gon) -- it's better if it's the concentrate rather than the spray. It doesn't matter if it rains later: it's those first few minutes when the still-living tissue is in contact with and soaking up the glyphosate or triclopyr that matters. Once the glyphosate/triclopyr has dried or the top layer of cells in the stump has died, no protection is needed.