The dynamic constitutive models based on viscous, elastic, and plastic elements often suffer from poor prediction performance and fail to fully capture the viscous, elastic, and plastic characteristics of cohesive soil. To address these limitations, a viscoelastic-plastic constitutive model for cohesive soil is proposed in this study by introducing a triggered viscoplastic element (symbolized as Ψ) and considering residual deformation as a starting point. The model takes into account the phenomena of vibration stabilization and vibration decay and is validated through dynamic triaxial shear tests. This dynamic constitutive model not only describes the development pattern of residual strain in cohesive soil under dynamic loads but also provides reasonable predictions for dynamic strain development. The results indicate that the viscosity coefficient of the Ψ element decays as the vibration period increases, and this attenuation is closely related to the moisture content under dynamic loading conditions. The optimal moisture content serves as an important parameter that influences both vibration stabilization and vibration decay. When the moisture content is less than the optimal moisture content, the deformation of the sample exhibits vibration stabilization, and the change of the viscosity coefficient can be ignored. When the moisture content is greater than the optimal moisture content, the deformation of the sample exhibits vibration decay, and the change of the viscosity coefficient cannot be neglected.