Eradicating blackberry vines may seem hopeless, especially if you don’t want
to use chemicals, but don’t give up just yet. The Northwest Center for
Alternatives to Pesticides advises gardeners to cut off the top growth, dig
out the main root-ball, and then follow-up by mowing all new growth.
Planting desirable plants to shade out the sun loving blackberries is also
critical. Read the NCAP’s blackberry management plan (pdf).