Medical report generation is crucial for clinical diagnosis and patient management, summarizing diagnoses and recommendations based on medical imaging. However, existing work often overlook the clinical pipeline involved in report writing, where physicians typically conduct an initial quick review followed by a detailed examination. Moreover, current alignment methods may lead to misaligned relationships. To address these issues, we propose DAMPER, a dual-stage framework for medical report generation that mimics the clinical pipeline of report writing in two stages. In the first stage, a MeSH-Guided Coarse-Grained Alignment (MCG) stage that aligns chest X-ray (CXR) image features with medical subject headings (MeSH) features to generate a rough keyphrase representation of the overall impression. In the second stage, a Hypergraph-Enhanced Fine-Grained Alignment (HFG) stage that constructs hypergraphs for image patches and report annotations, modeling high-order relationships within each modality and performing hypergraph matching to capture semantic correlations between image regions and textual phrases. Finally,the coarse-grained visual features, generated MeSH representations, and visual hypergraph features are fed into a report decoder to produce the final medical report. Extensive experiments on public datasets demonstrate the effectiveness of DAMPER in generating comprehensive and accurate medical reports, outperforming state-of-the-art methods across various evaluation metrics.