The evaluation of the shear performance of stone panel–panel joints (SPPJs) in stone cladding has important engineering significance, as it plays a crucial role in stone cladding failure. The purpose of this paper is to analyze and predict the influence of the dimension and the Young’s modulus of sealant on the shear performance of SPPJs. Based on monotonic and cyclic loading tests, the effects of Young’s modulus and the dimension of sealant on the failure characteristics, stress–strain characteristics, stiffness degradation, and energy dissipation capacity of an SPPJs were investigated. According to finite element analysis, the strain distribution of an SPPJ under monotonic loading was analyzed for different sealant widths and number of sealant layers. The results indicate that the failure modes of SPPJs change with the variation of sealant amount. As the Young’s modulus of the sealant increases, the shear failure strength and shear yield strain of SPPJs increase. The increase in sealant thickness reduces the shear failure strength and stiffness of SPPJs. Based on the same shear strain, the increase in the sealant thickness enhances the cumulative energy consumption of SPPJs. The strain concentration zone of the specimens with two sealant layers in unilateral SPPJs becomes larger with the increase in sealant width.