Climate Vulnerability Index (CVI) is used to assess the risk faced by a region due to global climate change. India is an especially climate vulnerable and spatially diverse region, which necessitates the development of improved, hyper-local assessment frameworks that can inform adaptation strategies. In this paper we present a deep-clustering based framework that generates latent representations of Indian block-level environmental, biophysical, and socio-economic features via a Beta Variational Autoencoder ( \(\beta \) -VAE). To interpret the complex, non-linear interrelationships among features captured in the latent space, we apply hierarchical clustering followed by tree-based SHapley Additive exPlanations (SHAP) explainers. We use the SHAP scores to present a novel computation of CVI, and then interpret these scores using Large Language Models (LLMs) to derive natural language cluster descriptions. We share our findings on the most vulnerable blocks, found primarily in states such as Bihar and Uttar Pradesh. We compare state-level climate mortality and economic risk rankings with our results and find that our method aligns more closely than existing Indian CVI rankings. The proposed framework reveals the advantages of machine learning approaches in assessing climate vulnerability.