Factors affecting the mechanical properties of the high-damping rubber plate mainly include temperature, shear strain rate, shear strain amplitude, and compressive stress. However, the existing studies focused on one factor and have not conducted detailed research on the coupling relationships between various factors. The influence on the mechanical properties of the high-damping rubber plate of one factor will change with the change in other factors. To study the coupling correlation, a series of horizontal cyclic loading tests were designed and carried out. Due to the simultaneous hyperelastic and viscoelastic properties of high-damping rubber, the hysteresis curve of the high-damping rubber plate is decomposed into a hyperelastic part and a damping part. Equations of the two parts are deduced by a theoretical method, and all the coefficients of the two parts are obtained by fitting the test results. Then, the variation coefficient is used to study the influence degree of each factor on these coefficients. Finally, the correlation variation coefficient is defined as the variation coefficient of variation coefficients and is used to quantify the coupling correlation between the factors. This study is of great significance in exploring the coupling correlation between the factors affecting the mechanical properties of the high-damping rubber plate.