Shape memory polymers (SMPs) have good properties of recovering their original shapes in the presence of an external stimulus. However, their thermodynamic behaviors behind the yielding effects on mechano-chemo-thermal shape-memory effect (SME) are yet explored. In this study, molecular entanglement theory is employed to develop a thermodynamic model in terms of glass transition temperature. Based on the Arrhenius equation and Adam-Gibbs theory, an extended yielding model is formulated to investigate the synergistic coordination of yield stress and stored strain energy on mechano-chemo-thermal SME and relaxation behavior in the amorphous SMPs. Furthermore, effectiveness of this model is demonstrated by applying it to predict thermomechanical and mechano-chemo-thermal shape recovery behaviors of the SMP, and the theoretical results are well validated by the experimental data reported in literature. This study explores the working principle of stored strain energy in terms of molecular entanglement and yield stress, and describes a constitutive relationship between molecular entanglement structure and mechano-chemo-thermal coupling thermodynamics in the amorphous SMP.