A mild steel-friction self-centering damper with a hybrid energy-dissipation mechanism (MS-SCFD) was proposed, which consisted of a mild steel, frictional, dual-energy-dissipation system and a disc spring resetting system. The structure and principle of the MS-SCFD were explained in detail while the restoring force model was established. The hysteretic behavior of the MS-SCFD under low-cycle reciprocating loading was modeled. Then, the influence of parameters such as the disc spring preload, the friction coefficient, and the soft-steel thickness on the mechanical properties of the MS-SCFD was investigated. The results indicate that the simulation results are basically consistent with the theoretical prediction results, with a maximum error of only 9.46% for the key points of bearing capacity. Since the MS-SCFD is provided with a hysteretic curve in the typical flag type, it will obtain the capacity of excellent self-centering performance. It can effectively enhance the stiffness, bearing capacity, and self-centering capability of the damper after the pre-pressure of the disc spring is increased. The energy-dissipation capacity of the MS-SCFD increases with the increase in the friction coefficient. However, it also increases the residual deformation of the MS-SCFD. The energy dissipation of the MS-SCFD is particularly sensitive to the thickness of mild steel. After being loaded, all components of the MS-SCFD are not damaged except for the plastic deformation caused by the yielding of the mild steel. The normal function of the MS-SCFD can be restored simply by replacing the mild steel plates after the earthquake. Therefore, it can significantly enhance the economy and applicability of the damper.