In conventional reinforced concrete and assembled monolithic concrete frame structures, considerable damage typically occurs in the beam–column joint zone under strong seismic activity. To improve seismic performance and earthquake resilience, a novel replaceable graded-yielding energy-dissipating connector (RGEC) for prefabricated concrete beam–column joints is proposed. In these joints, RGECs are assembled on the upper and lower sides of the beam end. These connectors enable the concentration of plastic deformation on their bending–shear components (BSCs) and buckling segment (BS). Consequently, structural seismic performance can be rapidly restored by replacing the RGECs after an earthquake. An RGEC can realize graded-yielding energy dissipation under earthquakes of different intensities with the successive yielding of BSCs and BS. Mechanical models of the BSC and BS are developed, and a series of tests is performed on 11 specimens. The tests examine the effects of key design factors (such as core plate thickness, width–thickness ratio of the BS, limit gap width, yield stress contour height ratio, and height–width ratio of the BSC) on the seismic behavior of the proposed damper. Results indicate that the RGEC exhibits excellent seismic performance in terms of strength capacity, deformation capacity, energy dissipation capacity, and stiffness degradation. The RGEC can effectively achieve energy dissipation through graded yielding under loads of multilevel intensities. Additionally, based on finite element models validated using available test data, the deformation behavior of the RGEC is analyzed by considering the influences of the yield stress contour height ratio and height–width ratio of the BSC, width–thickness ratio of the BS, and out-of-plane restraint gap width.