I raise Blueberries, and Blackberries, instead of raspberries, but I keep grasses to a minimum in both. With the Blueberries I mulch, heavily, and hand pull grasses (aka weeds). The Blackberries, being cane type plants, I just keep weeds cut back from the patch, and the few weeds that do come up among the canes I either pull up, or if not readily accessible let the canes smother it back.