Vision-language models (VLMs) enable open-vocabulary reasoning for robot manipulation, but their high inference latency limits responsiveness in dynamic scenes. Many scene changes, however, alter object geometry without invalidating task intent. We present DualManip, a dual-path framework that decouples infrequent semantic reasoning from responsive geometric adaptation. The semantic path decomposes the task and grounds task-relevant interactions, followed by a constraint-solving module for pose optimization. During execution, the geometric path continuously updates template-to-observation correspondences from live RGB-D observations via a shape-adaptive network. These correspondences transfer task-relevant grasp contacts across observations, enabling online grasp reconstruction under object motion and non-rigid deformation. The Information Interaction Module bridges the two paths by initializing task-relevant grasps from semantic grounding, validating geometric updates, and triggering semantic replanning upon update failures. Real-world evaluation spans six manipulation tasks covering non-rigid deformation, articulated reconfiguration, rigid motion, and high-precision assembly across three settings: static, single-change, and continuous dynamic. DualManip demonstrates superior manipulation robustness, particularly under continuous scene changes, while achieving geometric adaptation approximately 46$\times$ faster than agentic verification and semantic replanning. Our project page: https://lichengxi1.github.io/Dualmanip.

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