To investigate the compressive dynamic properties of hydraulic asphalt concrete under various temperatures, four temperatures and four strain rates have been set to perform the uniaxial compression experiments using hydraulic servo machine in this paper. The influence of temperature and strain rate on the failure modes, stress-strain curves and mechanical characteristic parameters of hydraulic asphalt concrete is analyzed and the results reveal that the failure modes and stress-strain curves have significant temperature effect. When the temperature is between −20 °C and 0 °C, the failure mode is dominated by brittle failure of asphalt binder, and hydraulic asphalt concrete shows obvious strain softening. With the addition of temperature, the failure modes of specimens are transferred from brittle failure to ductile failure since the asphalt changes from elastic-brittleness to viscoelasticity. Influenced by temperature effect, the compressive stress-strain curves of hydraulic asphalt concrete show strain hardening while the peak stress of hydraulic asphalt concrete is obviously decreased, and the variation coefficient of peak stress has a power relation with temperature. With successive increases in strain rate, the stress-strain curves of hydraulic asphalt concrete gradually are transferred from strain hardening to strain softening. The peak stress and stiffness modulus of specimens under compression gradually increase, and the dynamic increase factor of peak stress is linearly related with the logarithm value of strain rate after dimensionless treatment. In terms of the quantitative analysis of the experimental data, two relationship models of the coupling effect between temperature and strain rate are proposed. The proposed models have good applicability to the quantitative analysis of the experimental results in the manuscript. This paper offers important insights into the application and development of hydraulic asphalt concrete in hydraulic engineering.