To develop a new replaceable steel link with high energy dissipation capacity for establishing a rapid recoverable system of bridge piers, a novel demountable and replaceable low yield point steel links with corrugated web (LCSW link) is proposed. A series quasi-static test on six specimens was conducted to investigate their failure process and hysteretic behaviors, considering the effects of different material and shape of the webs, as well the height-to-span ratio of the replaceable link. The experimental results indicate that the LCSW links exhibit three types of failure modes: the local buckling of steel flanges, the welding fracture at flange-to-endplate connection, and the combination of welding fracture at flange-to-endplate connection and shear buckling of CSWs. The hysteretic behaviors of the specimens were mainly affected by the height-to-span ratio. Moreover, utilization of a small height-to-span ratio (1.7 in this paper) and low yield point steel (LYP160 steel) in the links improves the ductility and energy dissipation capacity. Three-dimensional nonlinear finite element models were established to simulate the hysteretic behavior of the LCSW links, and the yield strength and initial stiffness of the LCSW links under lateral loading were obtained through finite element simulation and simplified design method. The comparison of experimental and analytical results indicates that the finite element models were able to simulate the cyclic response well, and these proposed theoretical equations can be used efficiently to predict the capacity of LCSW links.