Breast cancer is a major global health concern, and mammography screening plays a central role in early detection. The large volume of screening examinations creates a substantial workload for radiologists, making accurate and consistent report generation a critical clinical challenge. Existing automated mammography report generation methods primarily focus on direct visual-to-text mapping, while overlooking the structured clinical reasoning process followed by radiologists in real-world practice. To address this limitation, we propose MammoRG, a mammography report generation framework that explicitly simulates the clinical reporting workflow by following the BI-RADS guideline and incorporating prior clinical knowledge to produce diagnostic reports. Specifically, MammoRG adopts a two-stage training framework. In the first stage, the model learns to integrate clinically relevant prior knowledge from a patient's four-view mammograms through classification-based supervision. In the second stage, a terminology-aware supervised fine-tuning strategy is introduced to model mammography-specific clinical terms as atomic semantic units, enabling the generation of high-quality reports with improved clinical consistency. To facilitate clinical efficacy evaluation of generated reports, we further develop MammoRGTool, a dedicated mammography report parsing tool that extracts structured clinical information from free-text reports. Extensive experiments demonstrate that MammoRG consistently outperforms existing methods across multiple clinical efficacy metrics, particularly in diagnosis-related BI-RADS F1, where it surpasses the second-best model by 2.73%, 2.04%, 1.90%, and 3.27% on the internal, external 1, external 2, and VinDr-Mammo datasets, respectively.