Road crashes claim over 1.3 million lives annually worldwide and incur global economic losses exceeding \$1.8 trillion. Such profound societal and financial impacts underscore the urgent need for road safety research that uncovers crash mechanisms and delivers actionable insights. Conventional statistical models and tree ensemble approaches typically rely on structured crash data, overlooking contextual nuances and struggling to capture complex relationships and underlying semantics. Moreover, these approaches tend to incur significant information loss, particularly in narrative elements related to multi-vehicle interactions, crash progression, and rare event characteristics. This study presents CrashSage, a novel Large Language Model (LLM)-centered framework designed to advance crash analysis and modeling through four key innovations. First, we introduce a tabular-to-text transformation strategy paired with relational data integration schema, enabling the conversion of raw, heterogeneous crash data into enriched, structured textual narratives that retain essential structural and relational context. Second, we apply context-aware data augmentation using a base LLM model to improve narrative coherence while preserving factual integrity. Third, we fine-tune the LLaMA3-8B model for crash severity inference, demonstrating superior performance over baseline approaches, including zero-shot, zero-shot with chain-of-thought prompting, and few-shot learning, with multiple models (GPT-4o, GPT-4o-mini, LLaMA3-70B). Finally, we employ a gradient-based explainability technique to elucidate model decisions at both the individual crash level and across broader risk factor dimensions. This interpretability mechanism enhances transparency and enables targeted road safety interventions by providing deeper insights into the most influential factors.