Timely nowcasting is critical for public safety during fast-evolving storms, where even short delays can trigger cascading failures—as in the October 2024 Spain flash flood that claimed over 90 lives within minutes. While radar offers reliable real-time sensing of atmospheric structure, models that collapse 3D volumes into 2D slices inevitably discard vertical information essential for capturing storm growth, phase transitions, and collapse. We introduce StormMind, a physically grounded framework that forecasts convective evolution by modeling causal interactions across stratified atmospheric layers. StormMind addresses two fundamental challenges:(1) the nonlinear, asynchronous coupling between low-, mid-, and high-level processes; and (2) reflectivity uncertainty, where storms with distinct vertical structures may appear deceptively similar on radar, masking their true phase and intensity. To tackle these issues, StormMind designs: i) a Convection Dynamics Extractor that models storm evolution from two complementary perspectives—horizontal morphology, capturing the spatial organization of physical processes within individual atmospheric layers, and vertical coupling, modeling energy exchanges across layers; and ii) a Convection Manifestation Reconstructor that adaptively fuses intra- and inter-layer signals, conditioned on the evolving storm state, to infer phase transitions (e.g., initiation, intensification, dissipation). Evaluated on the large-scale 3D-NEXRAD dataset (2020–2022, U.S.), StormMind outperforms strong baselines, achieving a 14.71% gain in CSI₄0. In real-world deployment with the Guangzhou Meteorological Bureau (Mar–May 2025), it improves CSI₄0 by 9.39% and boosts early-warning accuracy (98.33%)