The mechanical response of asphalt pavement under vehicular loading is an essential reference for crack-resistant pavement design. However, limited research focuses on the mechanical response measurement of asphalt pavement using a large-particle-size crushed stone base treated with fly ash and slag powder. Therefore, two types of asphalt pavements were constructed. The first type of asphalt pavement uses a large-particle-size crushed stone base treated with fly ash and slag powder, where the slag powder uses granulated blast furnace slag powder. The second type uses a conventional cement-stabilized crushed stone base and serves as a reference structure. Firstly, the strain gauges and temperature sensors were installed during the construction of asphalt pavements. Secondly, the mechanical response of the pavement was tested at different speeds and service time conditions. Then, sensitivity analysis and three-factor analysis of variance (ANOVA) were carried out. Finally, the prediction equations were developed. The results show that the longitudinal strain pulse of the asphalt layer exhibited a “compression–tension–compression” characteristic. For the transverse strain pulse of the asphalt layer, the base layer’s transverse and longitudinal strain pulses were only shown as “tensile” characteristics. The vehicular speed significantly affected the strain values for the base and asphalt layers, showing a decreasing trend with increasing speed. For the asphalt layer, the strain values showed an increasing trend with increasing temperature; for the base layer, the strain values showed a decreasing trend with increasing service time. The type of base layer had a significant effect on the strain value. Compared with the conventional base layer, the large-particle-size crushed stone base treated with fly ash and slag powder had lower strain at the base layer and a lower position of the asphalt layer, which could better prevent bottom-up fatigue cracking. Finally, the strain prediction model of the pavement under the speed and temperature (service time) was fitted to obtain a model that can predict the mechanical response of the pavement under different operating conditions. The findings of this research can provide a reference for the design of asphalt pavement using a large-particle-size crushed stone base treated with fly ash and slag powder.