Climate change adaptation requires the understanding of disruptive weather impacts on society, where large language models (LLMs) might be applicable. However, their effectiveness is under-explored due to the difficulty of high-quality corpus collection and the lack of available benchmarks. The climate-related events stored in regional newspapers record how communities adapted and recovered from disasters. However, the processing of the original corpus is non-trivial. In this study, we first develop a disruptive weather impact dataset with a four-stage well-crafted construction pipeline. Then, we propose WXImpactBench, the first benchmark for evaluating the capacity of LLMs on disruptive weather impacts. The benchmark involves two evaluation tasks, multi-label classification and ranking-based question answering. Extensive experiments on evaluating a set of LLMs provide first-hand analysis of the challenges in developing disruptive weather impact understanding and climate change adaptation systems. The constructed dataset and the code for the evaluation framework are available to help society protect against vulnerabilities from disasters.