Medical Anomaly Detection (MedAD) presents a significant opportunity to enhance diagnostic accuracy using Large Multimodal Models (LMMs) to interpret and answer questions based on medical images. However, the reliance on Supervised Fine-Tuning (SFT) on simplistic and fragmented datasets has hindered the development of models capable of plausible reasoning and robust multimodal generalization. To overcome this, we introduce MedAD-38K, the first large-scale, multi-modal, and multi-center benchmark for MedAD featuring diagnostic Chain-of-Thought (CoT) annotations alongside structured Visual Question-Answering (VQA) pairs. On this foundation, we propose a two-stage training framework. The first stage, Cognitive Injection, uses SFT to instill foundational medical knowledge and align the model with a structured think-then-answer paradigm. Given that standard policy optimization can produce reasoning that is disconnected from the final answer, the second stage incorporates Consistency Group Relative Policy Optimization (Con-GRPO). This novel algorithm incorporates a crucial consistency reward to ensure the generated reasoning process is relevant and logically coherent with the final diagnosis. Our proposed model, MedAD-R1, achieves state-of-the-art (SOTA) performance on the MedAD-38K benchmark, outperforming strong baselines by more than 10\%. This superior performance stems from its ability to generate transparent and logically consistent reasoning pathways, offering a promising approach to enhancing the trustworthiness and interpretability of AI for clinical decision support.