No. The berries grow on canes that grew in the last season and which haven’t previously fruited. Canes that have borne fruit in the last season will die off of their own accord before the next fruiting season (early summer), so the only thing that you need to do about dead wood is to remove it, carefully, because the youngberry and all of the worthwhile bramble berries plants such as boysenberries and silvanberries and marionberries have many tiny thorns all over their canes.
Of course, the other regular bit of maintenance that you need to do is to pick up long canes that are touching the ground and put them over your trellis, so that the ends of these canes don’t take root. It will all be worth it come summer.