Due to their weight, the seismic response control of buildings needs a large-scale damper. To reduce the consumption of shape memory alloys (SMAs), this study proposed a dual self-centering pattern accomplished by the coil springs and SMA, which could drive the energy dissipation device to recenter. Combined with the friction energy dissipation device (FD), the dual self-centering friction damper (D-SCFD) was designed, and the motivation and parameters were described. The mechanical properties of D-SCFD, including the simplified D-SCFD mechanical model, theoretical index calculations of recentering, and energy dissipation performance, were then investigated. The seismic response mitigation of the steel frame adopting the D-SCFDs under consecutive strong earthquakes was finally analyzed. The results showed that a decrease in the consumption of SMA by the dual self-centering pattern was feasible, especially in the case of low demand for the recentering performance. Reducing the D-SCFD’s recentering performance hardly affected the steel frame’s residual inter-story drift ratios when the residual deformation rate was less than 50%, which can help strengthen the controls on the steel frame’s peak seismic responses. It is recommended to utilize the D-SCFD with not too high a recentering performance to mitigate the seismic response of the structure.