Long chain-of-thought (Long CoT) reasoning improves performance on multi-step problems, but it also induces overthinking: models often continue generating after a correct solution has already been reached, producing redundant verification, backtracking, and other low-yield reasoning that increase inference cost and latency. This inefficiency is especially problematic in low-data fine-tuning regimes. We propose STOP (Structured On-policy Pruning), a unified on-policy framework for analyzing and pruning long-form reasoning traces. STOP has three components. First, it constructs self-distilled successful traces from the student model, reducing distributional mismatch relative to teacher-guided supervision. Second, it maps each trace into a structured reasoning interface through node segmentation, taxonomy annotation, and reasoning-tree construction. Third, on top of this interface, we introduce ECN (Earliest Correct Node), which retains the shortest prefix ending at the earliest node that both functions as an answering conclusion and yields the correct final answer, removing redundant post-solution reasoning while preserving semantic continuity. Experiments on DeepSeek-R1-Distill-Qwen-7B and DeepSeek-R1-Distill-LLaMA-3-8B across GSM8K, Math 500, and AIME 2024 show that STOP reduces generated tokens by 19.9–41.9% while largely preserving accuracy in low-data fine-tuning. Further analyses show that STOP does more than shorten traces: self-distilled ECN induces smaller distributional shift than teacher-guided pruning and reallocates reasoning effort away from redundant verification and backtracking toward more productive exploration.