Recycled concrete, which is formed by replacing coarse aggregates in ordinary concrete with recycled aggregates (RA), is of great significance for the secondary utilization of waste building resources. In civil engineering, concrete structures are sometimes subjected to a compression–shear multiaxial stress state. Therefore, research on the compression–shear multiaxial mechanical properties of recycled concrete plays an important role in engineering practice. To explore the effect of RA replacement rate on the compression–shear properties of recycled concrete, an experimental study was carried out using a compression–shear testing machine and considering five RA replacement rates and five axial compression ratios. Consequently, the failure modes and mechanical property parameters under different working conditions were obtained and were used to analyze the effects of RA replacement rate and axial compression ratio on the shear stress of recycled concrete. Eventually, the following conclusions were reached: With the growth of axial compression ratio, the shear cracks exhibit a developing trend along the oblique direction, and the friction traces on the shear surface are gradually deepened. As the replacement rate increases, the number of shear cracks is gradually increased, accompanied by increasing broken fragments falling off from the shear interface. Since the action of the axial compression ratio can effectively improve the mechanical bite force and friction on the shear interface of recycled concrete, as the axial compression ratio increases, the shear stress is gradually increased. On the other hand, due to the initial damage of RA and its weak adhesion with cement mortar, the shear stress is gradually reduced with the increase of RA replacement rate. Meanwhile, the increase in shear stress shows a gradually decreasing trend with the growth of axial compression ratio. Specifically, for the RA replacement rates of 0% and 100%, the shear stress increased by 4.06 times and 3.21 times, respectively, under the influence of the axial compression ratio. Under different axial compression ratios, the shear stress was reduced by 43~46%, due to the increase of RA replacement rate. In addition, based on the octahedral stress space and the principal stress space, a compression–shear multiaxial failure criterion and shear stress calculation model for recycled concrete were proposed, by considering the effect of the RA replacement rate. The outcomes of this research are of great significance for engineering applications and the development of recycled concrete.