Raspberries and blackberries produce fruit on 2 year old canes (stems/shoots). If you go look at your berry bushes, you’ll see the remains of the the canes that produced berries this year. Those cane grew last year and produced fruit this summer. They will look dried out and less vigorous. You’ll also see the new canes that grew over this summer. These are the canes that will flower and produce fruit next year so you don’t want to prune them off. Pruning can be done anytime after the fruiting period so go right ahead and prune of the old canes (the ones that made berries this year) since they will never make another berry. This is the annual cycle with blackberries and raspberries…always removing the canes that just finished making berries but leaving the fresh canes that will make berries next year.