Long chain-of-thought (Long CoT) reasoning improves performance on multi-step problems, but it also induces overthinking. This inefficiency is especially problematic in low-data fine-tuning regimes, where real applications adapt reasoning models with limited supervision and cannot rely on large-scale teacher distillation or heavy test-time control. To address this, we propose STOP (Structured On-policy Pruning), an on-policy algorithm for analyzing and pruning long-form reasoning traces. STOP constructs self-distilled traces from the model. Then it maps each trace into a structured reasoning interface through node segmentation, taxonomy annotation, and reasoning-tree construction. On top of this interface, we introduce ECN (Earliest Correct Node), which retains the shortest prefix ending at the earliest node. 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 19.4% to 42.4% while largely preserving accuracy in low-data fine-tuning. Beyond efficiency, our analyses show that STOP induces much smaller distributional shift than teacher-guided pruning, improves the structural efficiency of generated reasoning, and reallocates reasoning effort away from redundant verification and backtracking toward more productive exploration.