Recent advances in underwater networking exploit the large propagation delays in underwater channels to schedule transmissions which increase the performance of underwater acoustic sensor networks (UASNs). The underwater channel is broadcast in nature so it supports broadcast and multicast transmissions. In this paper, we discuss novel scheduling strategies, based on TDMA (Time Division Multiple Access), for UASNs where packets may be bound for multiple destinations. The main contributions are to establish an upper bound on the throughput of multicast networks, in which each packet has the same number of intended destinations, by exploiting large propagation delays, and explore network topologies that can achieve this bound. As an example, we study the throughput of unicast and multicast ring networks, including the properties of optimal, valid, perfect and fair transmission schedules. Further, several algorithms to find fair and optimal schedules for unicast and multicast ring networks are presented. Finally, we perform extensive simulations for uniform ring networks, as well as more general ring networks, in both noiseless and noisy underwater channels. Simulation results verify that the proposed algorithms can effectively determine the optimal schedules for ring networks, which achieve the maximum possible throughput and asymptotically approach the upper bound on the throughput of multicasting UASNs.