Against the backdrop of the suddenness and inherent uncertainty of emergencies, pre-disaster emergency facility location and emergency relief stockpiling are critical for improving the efficiency and sustainability of emergency response. This paper focuses on the emergency response network design problem considering uncertain transportation time and emergency demands. We cluster historical disaster events and extract cluster-specific statistical features, such as the average value, mean absolute deviation, and probabilistic statistical distance of uncertain parameters, constructing an ambiguity set based on the disaster feature and multivariate probability distribution information. Then, to minimize the total rescue cost, a feature-driven two-stage distributionally robust optimization model is formulated to determine reliable pre-disaster emergency facility locations, inventory decisions, and post-disaster resource allocation strategies. Finally, through an earthquake case in Sichuan Province of China, this work verifies that incorporating disaster clustering information enables a superior trade-off between the robustness and conservatism of emergency rescue decisions. Compared with the benchmark model, the proposed method displays better out-of-sample performance and can effectively enhance the sustainability of emergency response in uncertain environments.