Accelerated pavement testing (APT) is an effective method to study the long-term performance of pavement. Therefore, the dynamic strain behavior analysis of asphalt pavement has important guiding significance in the study of pavement failure modes. To explore the dynamic response of a high-content plant-mixed hot-reclaimed asphalt mixture under a dynamic load of vehicles, a full-scale test road was paved, and ALT biaxial accelerated loading test equipment was used to simulate the dynamic loads of vehicles. Based on parameters such as axle load, temperature, speed, and loading times, the development law for the bottom strain of the three pavement structures was analyzed. The test results show that the most unfavorable position of the asphalt pavement load is located just below the centerline of the wheel track on one side, and the damage effect of a single double-axle wheel load is far greater than that of two single-axle wheel loads. Then, the longitudinal tensile strain of the pavement bottom always maintains the alternating state of compression-tension and compression. The longitudinal tensile strain of the pavement bottom is larger than the transverse tensile strain, and transverse fatigue cracks appear first. Under normal temperature conditions, the bottom tensile strains of the three composite pavement structures under different axial loads are close, and the pavement performance of the hot-recycled asphalt pavement of structure A and structure B can meet the specification requirements. The relationship between the bottom strain and axle load is nonlinear and is directly related to the tire ground pressure, and the difference in the tensile and compressive strain values of the bottom of the three composite pavement structures is small. Under high temperature conditions, the bottom layer temperature of structure A and structure B is lower than that of structure C, and the thermal heat transfer efficiency of hot-recycled asphalt pavement is lower than that of ordinary asphalt pavement. Additionally, the longitudinal tensile strain is about 1–1.5 times that of the transverse tensile strain. Based on the Boltzmann function, the accumulative tensile strain prediction model was established to reflect the relationship between the cumulative strain at the bottom and the number of loads.