Recent multimodal large language models (MLLMs) and vision--language--action models have provided robots with new capabilities for long-horizon task understanding and planning. In surgical robotics, however, end-to-end prediction of low-level actions remains limited by insufficient precision, opaque decisions, and scarce data. This paper presents SurgiCLAW, a hierarchical skill-based framework for precision surgical manipulation. SurgiCLAW confines an MLLM to intraoperative visual understanding, structured explanation, and atomic surgical-skill selection, while delegating physical execution to verifiable deterministic control programs. For brain--machine-interface implantation, a representative high-precision surgical task, we construct a state-to-skill invocation dataset and expand it through visual and state perturbations. The model first learns structured skill invocation through supervised fine-tuning and is then optimized using three rewards for action correctness, operation prerequisites, and format validity, improving action selection, operational safety, and output parseability. We evaluate subtask success, offline model comparison, real-robot performance, and ablations. On a fixed test set, SurgiCLAW achieves 94.6% skill-selection accuracy and 93.0% macro-averaged F1 (Macro-F1). Across 50 closed-loop real-robot implantation trials, it achieves an 88.0% task success rate.

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