Safe autonomous driving in mixed traffic requires a unified understanding of multimodal interactions and dynamic planning under uncertainty. Existing learning-based methods often fail to capture rare but safety-critical behaviors, while rule-based systems lack adaptability in complex interactions. To address these limitations, we proposed CogDrive, a cognition-driven multimodal prediction-planning fusion framework that integrated explicit modal reasoning with safety-aware decision optimization. The prediction module introduced cognitive representations of interaction modes based on topological motion semantics and nearest-neighbor relational encoding. By incorporating a differentiable modal loss and multimodal Gaussian decoding, CogDrive effectively learned sparse and unbalanced interaction behaviors, improving long-tail trajectory prediction accuracy. The planning module was built upon an emergency-response concept and developed a safety-stabilized trajectory tree optimization. Short-term consistent root trajectories ensured safety within replanning cycles, while long-term branches provided smooth and collision-free avoidance under low-probability or rapidly switching modes. Experiments on the Argoverse 2 and INTERACTION datasets showed that CogDrive achieved state-of-the-art performance, reducing the minADE and miss rates while maintaining smoothness. Closed-loop simulations further confirmed stable and adaptive behavior across strong-interaction scenarios such as merging and intersections. By coupling cognitive multimodal prediction with safety-oriented planning, CogDrive establishes an interpretable and reliable paradigm for safe autonomy in complex traffic.