Predicting changes in binding free energy ($\Delta\Delta G$) is essential for understanding protein-protein interactions, which are critical in drug design and protein engineering. However, existing methods often rely on pre-trained knowledge and heuristic features, limiting their ability to accurately model complex mutation effects, particularly higher-order and many-body interactions. To address these challenges, we propose H3-DDG, a Hypergraph-driven Hierarchical network to capture Higher-order many-body interactions across multiple scales. By introducing a hierarchical communication mechanism, H3-DDG effectively models both local and global mutational effects. Experimental results demonstrate state-of-the-art performance on multiple benchmarks. On the SKEMPI v2 dataset, H3-DDG achieves a Pearson correlation of 0.75, improving multi-point mutations prediction by 12.10%. On the challenging BindingGYM dataset, it outperforms Prompt-DDG and BA-DDG by 62.61% and 34.26%, respectively. Ablation and efficiency analyses demonstrate its robustness and scalability, while a case study on SARS-CoV-2 antibodies highlights its practical value in improving binding affinity for therapeutic design.