The microstructural evolution of austenite during hot deformation determines the mechanical properties of steel products. Consequently, industrial applications necessitate a thorough comprehension and modeling of this process. Under varied hot deformation conditions, the flow stress, microstructure evolution, and constitutive modeling of a Cu-bearing steel were examined. At various temperatures and strain rates, compression experiments are conducted, and the resulting microstructures were studied by electron backscatter diffraction (EBSD). Our results indicate that fine prior austenite grains with an average diameter of 22.1 m and a high-angle grain boundary density of 0.25 m1 were produced at a deformation temperature of 950 °C and a strain rate of 1 s−1. The dominating rotating cube components ({001}<110>) in the sample deformed at 1150 °C were gradually replaced by the γ-fiber texture component as the deformation temperature decreased. To accurately predict the flow behavior of this steel, we proposed an improved Arrhenius constitutive model that accounts for strain rate and adiabatic temperature rise. With a correlation coefficient (Rc) of 0.9936, a root mean square error (RMSE) of 4.92%, and a relative error (δ) of 6.05 MPa, our results demonstrate that this model predicts the flow stress of the experimental steel with good precision. This research contributes to the development of high-performance steel products by shedding light on the microstructural evolution and flow behavior of Cu-containing steels under hot deformation conditions.