If you have picked all of the fruit and there is no sign of flowers then you can cut to the ground the canes that fruited (i.e., last year's canes). New canes (fast growing buggers...) should be left to ramble if you can stand it (just keep tips from rooting) until it's time for tying up in the Fall.

I wish my boysenberries were so helpful. They dribble out a harvest in this climate and seem to go on and on and on forever while everything becomes an increasing tangle.