Multi-modal multi-task learning holds significant promise in tackling complex diagnostic tasks and many significant medical imaging problems. It fulfills the needs in real-world diagnosis protocol to leverage information from different data sources and simultaneously perform mutually informative tasks. However, medical imaging domains introduce two key challenges: dynamic modality fusion and modality-task dependence. The quality and amount of task-related information from different modalities could vary significantly across patient samples, due to biological and demographic factors. Traditional fusion methods apply fixed combination strategies that fail to capture this dynamic relationship, potentially underutilizing modalities that carry stronger diagnostic signals for specific patients. Additionally, different clinical tasks may require dynamic feature selection and combination from various modalities, a phenomenon we term “modality-task dependence.” To address these issues, we propose M4oE, a novel Multi-modal Multi-task Mixture of Experts framework for precise Medical diagnosis. M4oE comprises Modality-Specific (MSoE) modules and a Modality-shared Modality-Task MoE (MToE) module. With collaboration from both modules, our model dynamically decomposes and learns distinct and shared information from different modalities and achieves dynamic fusion. MToE provides a joint probability model of modalities and tasks by using experts as a link and encourages experts to learn modality-task dependence via conditional mutual information loss. By doing so, M4oE offers sample and population-level interpretability of modality contributions. We evaluate M4oE on four public multi-modal medical benchmark datasets for solving two important medical diagnostic problems including breast cancer screening and retinal disease diagnosis. Results demonstrate our method's superiority over state-of-the-art methods under different metrics of classification and segmentation tasks like Accuracy, AUROC, AUPRC, and DICE.