According to the structure form of room and pillar goaf in gypsum mine, the mechanical model of pillar roof composite supporting structure was established in this research. Based on the cusp catastrophe theory and energy dissipation theory, the energy dissipation relationship of the support structure was analyzed, and a new instability criterion of the support system was derived by introducing the control parameters α and β. On this basis, the study of blasting caving was carried out. The influence of row spacing and hole depth on blasting caving was analyzed using ANSYS/LS DYNA software. The blasting influence range, stress wave attenuation and vibration velocity attenuation indices are obtained, and the blasting parameters such as the optimal distance and depth of blast holes between pillars and roof were optimized. Based on the results of theoretical analysis and numerical, combined with the engineering geological conditions of Dahan gypsum mine, the practical study of blasting caving was carried out. The caving scheme and caving sequence was determined, then the blasting caving effect was analyzed. The caving effect was found to be good, and the applicability of the theoretical model is verified.