This paper presents the mechanical properties of 100% recycled aggregate concrete (RAC), and the results and analysis of the dry–wet cycle accelerated sulfate attack test. The results show that recycled concrete aggregate (RCA) can replace the coarse and fine aggregate. The recycled clay brick aggregate (RCBA) is not suitable for use as a coarse aggregate because the water absorption exceeds the standard. RCA replaces the coarse aggregate; and RCBA returns the fine aggregate to prepare 100% recycled concrete aggregate (RAC). The water–cement ratio is the most significant factor affecting the compressive strength of 100% RAC. The results of the mechanical properties analysis show that the compressive strength of RAC is less than that of NAC, and the difference in compressive strength between 100% RAC and NAC decreases with age. The splitting tensile strength of 100% RAC was slightly higher than that of NAC except for 7 d. The results of the dry–wet cycle accelerated sulfate attack test showed that the performance of 100% RAC was lower than that of NAC under the dry–wet process and sulfate attack coupling. Still, the loss rate was less than 5%, which met the standard resistance to the dry–wet cycle accelerating the sulfate attack.