We present a novel multi-modal graph learning framework for competing risks survival analysis from electronic health records (EHRs). While recent work has demonstrated the power of deep learning for dynamic risk prediction, most models are constrained to unimodal inputs or static graph structures and cannot model competing clinical endpoints. We introduce a unified, end-to-end model that learns modality-specific spatio-temporal graph representations for time-series, demographics, diagnostic histories, and radiographic text, and fuses them via hierarchical attention into a global patient graph. This design enables dynamic construction of informative substructures both within and across modalities, offering interpretable predictions for multiple competing outcomes. We further propose a composite training objective combining survival likelihood, temporal ranking, and graph regularisation losses to improve risk discrimination, calibration, and structural consistency over time. Our model outperforms state-of-the-art baselines across five real-world EHR datasets, achieving up to 8\% gains in cause-specific concordance, while offering fine-grained interpretability across temporal and modality dimensions. These results establish a new foundation for trustworthy and data-efficient risk estimation in clinical settings.