Accurate prediction of binding free energy changes upon mutations is vital for optimizing drugs, designing proteins, understanding genetic diseases, and cost-effective virtual screening. While machine learning methods show promise in this domain, achieving accuracy and generalization across diverse data sets remains a challenge. This study introduces Geometric Graph Learning for Protein-Protein Interactions (GGL-PPI), a novel approach integrating geometric graph representation and machine learning to forecast mutation-induced binding free energy changes. GGL-PPI leverages atom-level graph coloring and multiscale weighted colored geometric subgraphs to capture structural features of biomolecules, demonstrating superior performance on three standard data sets, namely, AB-Bind, SKEMPI 1.0, and SKEMPI 2.0 data sets. The model's efficacy extends to predicting protein thermodynamic stability in a blind test set, providing unbiased predictions for both direct and reverse mutations and showcasing notable generalization. GGL-PPI's precision in predicting changes in binding free energy and stability due to mutations enhances our comprehension of protein complexes, offering valuable insights for drug design endeavors.