Late winter early spring is the best time to prune boxwoods. And yes, you can rejuvenate a boxwood shrub by cutting down into the dead zone. As long as there’s lots of sun in that area within about a year that shrub will have lots of new growth on the inside. if your boxwoods are not looking healthy, you need to call an arborist to come evaluate them for a disease. There are treatments for plenty of boxwood diseases and I’ve seen many clients have their boxwoods bounced back beautifully. However