In this work, we designed ternary ZnSnO3 particle-reinforced Cu matrix composites and evaluated the hot deformation behavior of ZnSnO3/Cu composites. The hot deformation characteristics of typical dynamic recrystallization were probed by the resulting true stress–strain curves of ZnSnO3/Cu composites. The influences of deformation conditions, including temperatures (650–850 °C) and strain rates (0.01–5 s−1), on the flow stress of the designed composites were investigated. This revealed that the peak stress increased with the increasing of strain rate and decreasing of temperature. Additionally, the activation energy was calculated to be 237.05 kJ/mol and followed by yielding a constitutive equation for low-stress ZnSnO3/Cu composites. The processing maps established by dynamic materials model theory indicated that the designed composites possessed excellent hot workability, and then the processing parameters (790–850 °C and 0.01–0.04 s−1) of the ZnSnO3/Cu composites were determined for practical industrial production. Our work discloses the deformation behavior of ZnSnO3/Cu matrix composites and extends the rational process design for ternary ceramic/metal materials with excellent hot workability.