In multi-hop underwater acoustic sensor networks (UWASNs), packet collisions due to hidden and local nodes adversely affect throughput, energy efficiency and end-to-end delay. Existing medium access control (MAC) protocols try to solve the problem by utilizing a single-phase contention resolution mechanism, which causes a large number of control packet exchanges and energy overhead. In this paper, we introduce a MAC protocol that splits this single-phase contention resolution mechanism into two phases to provide efficient multi-hop networking. In the first phase, local nodes are eliminated from the contention, and in the later phase, the adverse effects of hidden nodes are mitigated. This two-phased contention resolution provides higher energy efficiency, better throughput and shorter end-to-end delay, and it also enables adaptability for different network architectures. A probabilistic model of the proposed protocol is also developed to analyse the performance. The proposed protocol has been evaluated through quantitative analysis and simulation. Results obtained through quantitative analysis and simulation reveal that the proposed protocol achieves significantly better energy efficiency, higher and more stable throughput and lower end-to-end delay compared to existing protocols, namely T-Lohi and slotted floor acquisition multiple access (S-FAMA).