Against the backdrop of global warming and intensified anthropogenic activities, groundwater reserves are rapidly depleting and facing unprecedented threats to their long-term sustainability. Consequently, investigating groundwater reserves is of critical importance for ensuring water security and promoting sustainable development. This study takes the Heilongjiang (Amur) River Basin as the research area. Groundwater storage was estimated using data from the Gravity Recovery and Climate Experiment (GRACE) satellite and the Global Land Data Assimilation System (GLDAS) covering the period from 2002 to 2024. A combination of Random Forest (RF), SHapley Additive exPlanation (SHAP) models, and Pearson partial correlation coefficients was employed to analyze the spatiotemporal evolution characteristics, driving mechanisms, and spatial linear correlations of the primary influencing factors. The results indicate that the basin’s groundwater storage anomaly (GWSA) exhibits an overall declining trend. GWSA is influenced by multiple factors, including climatic and anthropogenic drivers, with temperature (TEM) and precipitation (PRE) identified as the primary controlling variables. Spatiotemporal analysis reveals significant spatial heterogeneity in the relationship between GWSA evolution and its primary drivers. This study adopts a “retrieval–attribution–spatial analysis” framework to provide a scientific basis for enhancing regional groundwater security and supporting sustainable development goals.