The Chushandian Reservoir, a key control project on the Huaihe River, is vital for flood control, water allocation, and maintaining ecological baseflow. This study analyzes runoff evolution and provides predictive insights for sustainable water management. Methods employed include Extremum Symmetric Mode Decomposition (ESMD) for decomposing complex signals, a mutation detection algorithm to identify significant changes in time-series data, and cross-wavelet transform to examine correlations and phase relationships between time series across frequencies. Additionally, the hybrid models GM-BP and CNN-LSTM were used for runoff forecasting. Results show cyclical fluctuations in annual runoff every 2.3, 5.3, and 14.5 years, with a significant decrease observed in 2010. Among climate factors, the Atlantic Multidecadal Oscillation (AMO) had the strongest correlation with runoff variability, while ENSO and PDO showed more localized impacts. Model evaluations indicated strong predictive performance, with Nash–Sutcliffe Efficiency (NSE) scores of 0.884 for GM-BP and 0.909 for CNN-LSTM. These findings clarify the climatic drivers of runoff variability and provide valuable tools for water resource management at the Chushandian Reservoir under future climate uncertainties.