Adding rubber into sands has been found to improve the mechanical behavior of sands, including their dynamic properties. However, ambiguous and even contradictory results have been reported regarding the dynamic behavior of sand–rubber mixtures, particularly in terms of the damping ratio. A series of cyclic triaxial tests were, therefore, performed under a large range of shear strains on sand–rubber mixtures with varying rubber volume contents, rubber particle sizes, and confining pressures. The results indicate the dynamic shear modulus decreases with increasing rubber volume content and with decreasing particle size and confining pressure. The relationship of the damping ratio to the evaluated parameters is complicated and strain-dependent; at shear strains less than a critical value, the damping ratio increases with increasing rubber volume content, whereas the opposite trend is observed at greater shear strains. Furthermore, sand–rubber mixtures with different rubber particle sizes exceed the damping ratio of pure sand at different rubber volume contents. A new empirical model to predict the maximum shear moduli of mixtures with various rubber volume contents, rubber particle sizes, and confining pressures is accordingly proposed. This study provides a reference for the design of sand–rubber mixtures in engineering applications.