Differences in thermal contraction/expansion and volume changes during discharge/charge cycles lead to internal stresses that ultimately cause degradation of solid-state composite cathodes and hinder the realization of their practical applications. We employ the smoothed boundary method to solve the mechanical equilibrium equation for the residual stresses induced by cooling from the sintering temperature and by (de)lithiation in polycrystalline composite microstructures that are similar to realistic solid-state composite cathodes. The overall deformations of the composite slabs under these fabrication and operation conditions are also evaluated. The effects of cathode thickness and selections of different cathode materials on the resulting residual stresses and deformations are examined. We find that the (de)lithiation stresses during cycling are more than twice the thermal residual stresses after sintering. Furthermore, the maximum (de)lithiation and thermal residual stresses are sensitive to the cathode thickness only when the cathode-layer thickness is comparable to that of the electrolyte separator layer. We also investigate the impact of the lithium site fraction of the cathode particles prior to sintering on the cycling stresses and deformations, which may pave the path toward an approach to mitigating mechanically induced degradation.