We present the eruption of a mini-filament that caused a large-scale complicated coronal mass ejection (CME) on 2014 March 28, using the high-resolution observations taken by the Solar Dynamic Observatory. Three-dimensional coronal magnetic field extrapolated from the nonlinear force-free field code reveals that the magnetic environment of the eruption source region was a large fan-spine magnetic system that hosted another small fan-spine system under its fan, and the mini-filament was located under the fan structure of the small fan-spine system. Our analysis results suggest that the eruption of the mini-filament underwent three reconnection processes before the formation of the CME. First, the erupting filament triggered the null point reconnection in the small fan-spine system. During this stage, the sudden expansion of the spine field lines also excited a large-scale extreme-ultraviolet wave. Second, the spine field lines of the small fan-spine system were pushed up by the erupting filament and therefore further triggered the null point reconnection in the large fan-spine magnetic system. Third, during the second stage, magnetic reconnection also occurred between the two legs of the stretched confining field lines of the mini-filament. The present study suggests that the formation of the observed CME from the coupling fan-spine magnetic system was more complicated than previously thought, needing to undergo multistage magnetic reconnection processes in the low corona.