Multicasting is becoming more and more important in the Internet of Things (IoT) and wearable applications (e.g., high definition video streaming, virtual reality gaming, public safety, among others) that require high bandwidth efficiency and low energy consumption. In this regard, millimeter wave (mmWave) communications can play a crucial role to efficiently disseminate large volumes of data as well as to enhance the throughput gain in fifth-generation (5G) and beyond networks. There are, however, challenges to face in view of providing multicast services with high data rates under the conditions of short propagation range caused by high path loss at mmWave frequencies. Indeed, the strong directionality required at extremely high frequency bands excludes the possibility of serving all multicast users via a single transmission. Therefore, multicasting in directional systems consists of a sequence of beamformed transmissions to serve all multicast group members, subgroup by subgroup. This paper focuses on multicast data transmission optimization in terms of throughput and, hence, of the energy efficiency of resource-constrained devices such as wearables, running their resource-hungry applications. In particular, we provide a means to perform the beam switching and propose a radio resource management (RRM) policy that can determine the number and width of the beams required to deliver the multicast content to all interested users. Achieved simulation results show that the proposed RRM policy significantly improves network throughput with respect to benchmark approaches. It also achieves a high gain in energy efficiency over unicast and multicast with fixed predefined beams.