In order to investigate the influence of the coupling effect of sodium sulfate dry-wet (DW) cycles on the mechanical properties of carbon-polyvinyl alcohol hybrid fiber reinforced recycled coarse aggregate concrete (HFRAC), HFRAC specimens were subjected to uniaxial compression tests. The total volume fraction of fibers was kept constant at 0.4%, and various volume fractions of carbon fibers (CF) were added to the recycled coarse aggregate concrete (RAC), namely 0%, 0.1%, 0.2%, 0.3%, and 0.4%, with polyvinyl alcohol (PVA) fibers replacing a portion of CF in equivalent volume. Uniaxial compressive stress–strain curves were obtained for HFRAC specimens subjected to different numbers of DW cycles (0, 30, 60, and 120 cycles). Microscopic testing methods including acoustic emission (AE), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD), and nuclear magnetic resonance (NMR) were employed to analyze the microstructure, erosion product composition, and pore structure changes of the specimens. The results revealed that, for RAC specimens, the peak stress (σp) and elastic modulus (E) initially increased and then decreased, whereas the peak strain (εp) initially decreased and then increased with an increase in the number of DW cycles. After adding hybrid fibers, the σp values of CF, Hybrid 3:1, Hybrid 1:1, Hybrid 1:3, and PVA specimens increased (or decreased) by 12.0%, 11.43%, 0.9%, −9.5%, and −8.5%, respectively, compared to RAC. The Hybrid 1:3 specimen exhibited a negative hybrid effect. With an increase in the erosion age, the Hybrid 3:1 specimen demonstrated enhanced resistance to sulfate attack and achieved the highest σp value after 120 cycles. The influence of sulfate DW cycles coupling on the microscopic damage mechanism of HFRAC was analyzed using a statistical damage constitutive model. The microscopic damage evolution process was characterized by five characteristic parameters: E0, εa, εh, εb, and H. The analysis results indicated a clear correlation between the variation of these characteristic parameters and the number of DW cycles. An effective connection was established between the microscopic damage mechanism and the macroscopic nonlinear constitutive behavior. The phenomenon of relative lagging of acoustic emission signals during the uniaxial compression process was explained from the perspective of effective stress. This study provides a theoretical basis for the promotion and application of RAC under sulfate DW cycle environments.