While coronary imaging is widely used for anatomical assessment, CCTA reports play a distinct last-mile role in clinical care. Ratherthan serving as an intermediate signal, CCTA provides an assessment of coronary disease severity (known as the CAD-RADS score) toguide patient management. However, real-world clinical text exhibits substantial heterogeneity in terminology and structure, leadingto inconsistent interpretation by automated systems, even for clinically similar cases. Recent work leverages a direct application ofLLMs for automated CAD-RADS scoring, but is limited by small, non-public, and homogeneous clinical data. We introduce CCTA-RADS, the largest publicly available dataset of 940 real-world CCTA reports from a major cardiovascular center, each annotated with CAD-RADS scores. Our analysis reveals that direct approaches, including state-of-the-art LLMs (GPT-4o, GPT-o3) and fine-tuned BERT models underperform on diverse real-world clinical data. To address these limitations, we propose a two-stage pipeline that decouples structuring from classification: an LLM-based parser normalizes heterogeneous reports into structured format, followed by fine-tuned BERT classification. This approach substantially improves the F1-score by 6%-13% compared with direct methods. We deploy our system as an interactive web interface that allows clinicians to upload CCTA reports for automated CAD-RADS assessment with SHAP and LIME explainability visualizations.