While safety alignment and guardrails help large language models (LLMs) avoid harmful outputs, they can also induce overrefusal, i.e., unwarranted rejection of benign queries that merely appear risky. We present DDOR (Delta Debugging for OverRefusal), a fully automated and explainable framework for overrefusal testing and repair in a black-box setting, where only model inputs and outputs are accessible and internal safety mechanisms remain opaque. DDOR applies delta debugging to localize minimal refusal-triggering fragments (mRTFs) that provide phrase-level, explainable evidence for why a refusal occurs. Conditioned on these mRTFs, DDOR generates diverse, context-rich prompts and performs multi-oracle validation to filter intrinsically unsafe or ambiguous cases, producing scalable and model-specific overrefusal test suites (approximately 1K cases per model). Beyond evaluation, we further leverage localized mRTFs to perform targeted prompt repair, substantially reducing overrefusal while preserving the original intent and maintaining safety on genuinely harmful inputs. Overall, DDOR offers a practical end-to-end solution to both evaluate and mitigate overrefusal, improving LLM usability without sacrificing safety.