To address the weak interfacial transition zone and insufficient mechanical properties of recycled aggregate pervious concrete, this study proposes a dual modification strategy using basalt fibers and ultra-fine mineral powder. The macroscopic mechanical and hydraulic properties of the material were analyzed through orthogonal experiments. Techniques including X-ray diffraction, scanning electron microscopy, and micro-computed tomography were employed to systematically reveal the microstructural evolution and internal pore network topology of the modified system. Based on range analysis of mechanical stiffness and drainage efficiency, the optimal mix proportions were determined as 5–10 mm aggregate, a water–cement ratio of 0.31, and a fiber content of 0.50%. Microscopic tests confirm that the pozzolanic reaction of ultra-fine mineral powder increases matrix density and enhances the shear bond strength between fibers and the cement paste, enabling the physical bridging effect of basalt fibers. The dual modification exhibits a synergistic effect on load-bearing capacity and crack resistance. CT scan results show that the internal pore cross-sectional area follows a unimodal skewed distribution, with the characteristic distribution peak located at 3.5 mm². This homogeneous microporous network limits the critical defect size, optimizing the stress transfer path while ensuring fluid transport.