Controlling blackberry before doing a no dig garden

by mama mia
(woodacre, california)

the dreaded blackberry bushes!

hi, we live in northern california and have half an acre of south facing property, a bit sloping, and i am getting ready to make my no-dig garden with the layers, etc - i'm so excited and have all my little seedlings starting to sprout on the kitchen counter...

my one question is the about the blackberry bushes. about half of the gardening space is overgrown with them. can i cut them down to the roots and start the layers at ground level? or do i have to pull out the roots... please say i don't have to pull out the roots... :)

thanks for any advice!
mia