Rutting is one of the most widespread and severe diseases in the service life of asphalt pavement. Enhancing the high-temperature rheological properties of pavement materials is one of the valid measures that can be used to solve rutting disease. In this research, the laboratory tests were carried out to compare the rheological properties of the different asphalts (including neat asphalt (NA), styrene–butadiene–styrene asphalt (SA), polyethylene asphalt (EA), and rock-compound-additive-modified asphalt (RCA)). Then, the mechanical behaviors of different asphalt mixtures were investigated. The results show that the rheological properties of modified asphalt with a 15% rock compound additive performed better compared with the other forms of modified asphalt. The dynamic shear modulus of 15% RCA is significantly higher than the other three asphalt binders, which is 8.2 times, 8.6 times, and 14.3 times that of the NA, SA, and EA at a temperature of 40 °C, respectively. After adding the rock compound additive, the compressive strength, splitting strength, and fatigue life of the asphalt mixtures were significantly enhanced. The results of this research have practical significance for new materials and structures to improve asphalt pavement resistance to rutting.