The dynamic response of freeze-thaw tailings dam has attracted worldwide attention because of the increasing mining scale and frequent earthquake activity in cold regions. According to the experimental observations, the dynamic mechanical behaviors and failure mechanisms of the freeze-thaw tailings are reinterpreted, and a dynamic constitutive model for the material is established by utilizing homogenization theory. In this model's framework, tailings are regarded as quasi-continuous materials. Their representative volume element is conceptualized as a binary-medium structure composed of bonded elements with elastic-brittle properties and frictional elements with elastoplastic features. The former can gradually break into the latter upon cyclic loading, and both of the two components contribute to the overall capacity. Subsequently, a strain concentration tensor is adopted to describe the relationship between the local mechanical behaviors and average macro features. The model parameters are determined based on the experimental results. Comparisons between the computed and tested results are discussed specifically in aspects of the evolution of stress, strain and pore pressure. The results show that the model can capture the main features on predicting the dynamic response of tailings. In addition, it reflects the effects of freeze-thaw cycles, confining pressures and cyclical shear stress ratios on the dynamic features.