A solar jet that occurred on 2014 July 31, which was accompanied by a GOES C1.3 flare and a mini-filament eruption at the jet base, was studied by using observations taken by the New Vacuum Solar Telescope and the Solar Dynamic Observatory. Magnetic field extrapolation revealed that the jet was confined in a fan-spine magnetic system that hosts a null point at the height of about 9 Mm from the solar surface. An inner flare ribbon surrounded by an outer circular ribbon and a remote ribbon were observed to be associated with the eruption, in which the inner and remote ribbons, respectively located at the footprints of the inner and outer spines, while the circular one manifested the footprint of the fan structure. It is worth noting that the west part of the circular ribbon exhibited an interesting round-trip slipping motion, while the inner ribbon and the circular ribbon’s east part displayed a northward slipping motion. Our analysis results indicate that the slipping motions of the inner and the circular flare ribbons reflected the slipping magnetic reconnection process in the fan’s quasi-separatrix layer, while the remote ribbon was associated with the magnetic reconnection at the null point. In addition, the filament eruption was probably triggered by the magnetic cancellation around its south end, which further drove the slipping reconnection in the fan quasi-separatrix layer and the reconnection at the null point.