Modelling multi-shape memory effect (multi-SME) of shape memory polymers (SMPs) is a critical challenge for fields of mathematics/statistics and condensed-matter physics. These SMPs have a huge number of segments and their thermomechanical behaviors are determined by heating history and cooperative relaxations (e.g., relaxation of all segments occurs simultaneously). In this study, a one-dimensional coupling model was proposed to investigate the cooperative dynamics of multiple glass transitions and thermomechanical behaviors of the SMPs. The overall relaxation behaviors of different tangled segments in the SMPs were formulated based on the Boltzmann's superposition principle by coupling the highest transition temperature (T max) and initial transition temperature (T min) of all segments. Dependences of thermomechanical properties and relaxation strains upon the parameters of T max, T min, relaxation time and heating rate were theoretically investigated. Multiple glass transitions, thermomechanical and shape memory behaviors of the SMPs have been well described using this newly proposed coupling model. Finally, the simulation results were compared with the experimental data, and good agreements between them were obtained.