The Indonesian Throughflow (ITF) is a key oceanic pathway connecting the Pacific and Indian Oceans, exerting important influences on regional air–sea interactions, heat and salt transport, and global climate variability. However, multi-channel ITF transport is jointly regulated by multiple physical processes, including regional sea surface height, wind forcing, and density stratification. Its dominant controlling factors and lagged response mechanisms remain difficult to directly identify from traditional statistical models or black-box prediction models. To address this issue, this study develops an interpretable neural causal discovery framework for multi-channel ITF transport prediction. The framework organizes regional sea surface height (SSH), wind stress, and density stratification proxy variables into a physically meaningful candidate causal-edge space, and learns potential causal dependencies among source variables, lag windows, and transport channels through a lag-window-level Neural Granger mechanism. Furthermore, this study adopts a cross-random-seed gradient attribution stability screening strategy to extract stable and sparse causal candidate edges, and retrains the prediction model using stable-edge masks, thereby improving the reliability and physical consistency of causal interpretation while maintaining predictive skill. The experimental results show that stable causal-edge constraints can substantially reduce the number of candidate edges while maintaining or improving model prediction performance. Cross-seed stable edge screening further reveals that different ITF transport channels exhibit significant differences in their dominant controlling factors and lagged response scales, indicating channel-specific dynamical regulation structures among ITF branches. This framework not only provides a physically guided and interpretable modeling approach for multi-channel ITF transport prediction, but also offers a new technical pathway for data-driven causal mechanism identification in complex ocean circulation systems.