In order to address the discontinuous energy dissipation and poor adaptability to continuous variations in ground motion intensity commonly observed in traditional single-stage or multi-stage yielding metallic dampers, a continuous yielding replaceable mild steel damper (CYRMSD) was proposed in this study. Quasi-static tests were first conducted to investigate the replaceability, continuous yielding characteristics, and failure modes of the CYRMSD. A three-stage mechanical model considering combined translational-rotational deformation was then established, and theoretical formulas for key parameters were derived. Finite element simulations were subsequently employed to validate the accuracy of the proposed model, and the effects of geometric parameters on the mechanical performance were systematically analyzed. Finally, elastoplastic time-history analysis and design method validation were carried out based on a practical engineering project. The results show that the CYRMSD can be conveniently replaced after damage. Compared with multi-stage yielding mild steel dampers, the CYRMSD exhibits superior energy dissipation capacity and enables continuous yielding. The numerical simulations agree well with the experimental data, and the theoretical formulas yield calculation errors of less than 6.3%, demonstrating their reliability in predicting the mechanical behavior of the CYRMSD. The seismic reduction ratio of the structure equipped with the CYRMSD exceeds 40%, and the hysteretic curve characteristics indicate stable continuous yielding performance under minor, moderate, and major earthquake conditions. It is concluded that the CYRMSD combines the advantages of continuous yielding energy dissipation and post-earthquake replaceability, effectively enhancing the seismic energy dissipation capacity of reinforced concrete frame structures under multiple earthquake intensity levels, and showing promising prospects for engineering applications.