Medical multimodal reasoning models are typically trained on teacher-generated rationales, discarding the valid reasoning in students' own failed trajectories, while general-domain correction methods offer little guidance for errors in image reading, anatomical context, or differential diagnosis. We propose MedEvo, which uses medical knowledge, namely a tag taxonomy and error-type diagnosis, to navigate both trajectory repair and data selection. For each failed rollout, a gold-blind auditor locates the first consequential error and provides a minimal, answer-free hint; the same student retains the valid prefix and regenerates the erroneous suffix. After each round, MedEvo identifies capability gaps across medical tags on a held-out feedback set and prioritizes related questions for new rollouts and repairs. With supervised fine-tuning (SFT) alone, MedEvo raises Qwen3.5-9B mean accuracy across seven benchmarks from 65.57% to 69.12% (47.40% to 54.50% on the multimodal track of MedXpertQA (MedXpertQA-MM)), surpassing teacher-distillation SFT (66.93%). It also raises Qwen3.5-35B and Qwen3.5-397B mean accuracy from 67.91% to 73.04% and from 71.83% to 74.95%, respectively. Our analyses show that failed trajectories contain reasoning worth preserving, that repair success does not imply learning value, and that independent feedback is key to sustained improvement.

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