Safe autonomous driving in mixed traffic requires a unified understanding of multimodal interactions and dynamic planning under uncertainty. Existing learning based approaches struggle to capture rare but safety critical behaviors, while rule based systems often lack adaptability in complex interactions. To address these limitations, CogDrive introduces a cognition driven multimodal prediction and planning framework that integrates explicit modal reasoning with safety aware trajectory optimization. The prediction module adopts cognitive representations of interaction modes based on topological motion semantics and nearest neighbor relational encoding. With a differentiable modal loss and multimodal Gaussian decoding, CogDrive learns sparse and unbalanced interaction behaviors and improves long horizon trajectory prediction. The planning module incorporates an emergency response concept and optimizes safety stabilized trajectories, where short term consistent branches ensure safety during replanning cycles and long term branches support smooth and collision free motion under low probability switching modes. Experiments on Argoverse2 and INTERACTION datasets show that CogDrive achieves strong performance in trajectory accuracy and miss rate, while closed loop simulations confirm adaptive behavior in merge and intersection scenarios. By combining cognitive multimodal prediction with safety oriented planning, CogDrive offers an interpretable and reliable paradigm for safe autonomy in complex traffic.