Cognitive acoustic (CA) is emerging as a promising technique for environment-friendly and spectrum-efficient underwater acoustic networks (UANs). Due to the unique features of UANs, traditional spectrum management systems used for radio networks need an overhaul to work efficiently in underwater environments. In this paper, we propose a receiver-initiated spectrum management (RISM) system for underwater cognitive acoustic networks (UCANs). RISM seeks to significantly improve the performance of UANs through a collaboration of the physical layer and medium access control (MAC) layer. This system features collaborative spectrum sensing, efficient spectrum sharing and advanced spectrum decision algorithms. It aims to provide collision-free data transmissions and efficient spectrum utilization for CA users, while avoiding harmful interference with both “natural acoustic systems”, such as marine mammals, and “artificial acoustic systems”, like sonar users and other UANs. Simulation results show that, RISM can effectively operate in both tree topology and partially connected mesh topology networks and achieve collision-free data transmissions.