Rubber–sand mixtures are an excellent alternative backfill material in geotechnical engineering. To study the dynamic shear characteristics of the geogrid and rubber–sand mixture interface, cyclic direct shear tests were conducted to analyse the effects of rubber content, particle size ratio (r), normal stress, and shear displacement amplitude (A). The variation law of shear stiffness and damping ratio was also analysed. The results revealed that, as the rubber content increased, the shape of the hysteresis loop evolved from a full fusiform to a flat state; as r decreased, the hysteresis loop became flatter. The peak shear stress was the largest (increased by 5.4%–15.7%) when the rubber content was 10%. When the rubber contents were 10% and 30%, as r increased, the interface peak shear stress increased. The geogrid and rubber–sand mixture interface exhibited shear hardening when A = 3 mm and shear softening when A = 12 mm. When A = 6 mm, the interface with rubber contents of 10%, 30% and 50% tended to transition from shear softening to shear hardening. The damping ratio was the largest (increased by 9.3%) when the rubber content was 10%. Additionally, as r increased, the shear stiffness and damping ratio increased.