Structures or chemical engineering facilities can be subjected to the combined effects of sulfate corrosion and high temperature in the event of fire. This paper presents experimental results on compressive stress–strain relationships of recycled coarse aggregate concrete (RAC) and normal aggregate concrete (NAC) after dry–wet cycles of sulfate corrosion and high-temperature exposure. First, RAC and NAC specimens were subjected to 0, 20, 40, 60, 80, 100, and 120 dry–wet cycles of sulfate corrosion, respectively. Then, RAC and NAC specimens were subjected to 0 °C, 200 °C, 400 °C, 600 °C, and 800 °C temperature exposures, respectively. At last, RAC and NAC specimens were loaded by uniaxial compressive test. The test results show that the shapes of the stress–strain curves of RAC and NAC specimens after the 200 °C exposure and dry–wet cycles of sulfate corrosion were basically the same as those at room temperature. When the temperature was in the range of 200–400 °C, the elastic modulus and peak stress of RAC decreased with the number of dry–wet cycles of sulfate corrosion, while the corresponding peak strain gradually increased. When the temperature was lower than 400 °C, the number of dry–wet cycles of sulfate corrosion had a greater impact on the peak strain of RAC, while the temperature had a greater impact on the peak strain of RAC when the temperature exceeded 400 °C. After the temperature exceeded 400 °C, the elastic part in the ascending section of the stress–strain curve of RAC gradually shortened, and the peak point of the curve also shifted significantly to the lower right. The increase in peak strain of the RAC was larger than that of NAC. Based on the test results, a compressive stress–strain relationship model of RAC after sulfate corrosion and high temperature is established.