To address the core problem that fixed modulation and coding schemes suffer from low transmission efficiency caused by the strong spatio-temporal dynamic characteristics of time-varying underwater acoustic (UWA) channels, and existing adaptive modulation technologies can hardly simultaneously balance the transmission constraints of channel throughput, energy efficiency and Bit Error Rate (BER) in mobile UWA scenarios, this paper proposes an adaptive modulation and coding method for Orthogonal Time Frequency Space (OTFS) UWA communications based on Deep Deterministic Policy Gradient (DDPG). This method models the adaptive modulation decision-making process as a Markov decision process (MDP) with unknown state transition probability, designs a two-stream parallel feature extraction architecture to fuse multi-dimensional channel features, and introduces an additive attention mechanism to dynamically adjust the weight of the reward function, so as to realize the adaptive balance between channel throughput and energy efficiency. The channel simulation results based on the real hydrological scenario of Danjiangkou Reservoir show that the proposed method achieves an average channel throughput of 2.54 Mbit·s-1 after convergence, which is 7.6% higher than that of the Deep Q-Network, with an average energy efficiency improvement of 5.6%. The BER compliance rate can still reach 0.76 under harsh channel conditions, and its comprehensive performance is significantly better than that of mainstream algorithms including Proximal Policy Optimization and the original Deep Deterministic Policy Gradient. This work can provide reliable technical support for adaptive transmission of mobile underwater acoustic communications.