By integrating the Fox–Flory equation and the rubber elasticity principle, a phenomenologically constitutive model was proposed in this study to describe high mechanical recovery strength and a tailorable shape transition behavior of shape memory polymer (SMP) copolymers. The thermodynamics of different monomers in the copolymers were formulated by considering their influences on glass-transition temperatures (Tg) and elastic moduli based on the Fox–Flory and Gordon–Taylor equations. Effects of the Tg, weight fraction, molecular weight, storage modulus, and rubbery modulus of various monomers on thermomechanical and shape recovery behaviors of the SMP copolymers were theoretically investigated and discussed. Working principles of enhanced mechanical strength and a tailorable shape transition behavior of the SMP copolymers have been well-described using this newly proposed model, which offers an effective strategy for designing SMPs with high mechanical strength and a desirable shape memory behavior. Furthermore, molecular dynamics simulations were used to predict the glass-transition temperature from a molecular scale and the experimental results fit well with our modeling results.