We present observations of the eruption and then reformation of a filament caused by its nearby emerging magnetic flux. Driven by the emerging magnetic flux, the emerging positive fluxes moved toward and canceled with their nearby negative fluxes, where the negative ends of a filament channel beneath the filament and a bundle of left-skewed coronal loops overlying the filament were anchored. Complemented by the nonlinear force-free field extrapolation, we find that the coronal magnetic field lines associated with the filament channel and the emerging magnetic fields consist of sheared field lines. Prior to the filament eruption, unambiguous observational evidence indicates that multiple interactions occurred between the emerging magnetic fields and the left-skewed coronal loops, implying a tether-weakening reconnection. Specifically, during the final episode of the tether-weakening reconnection, a remarkable sigmoid structure was formed and lifted up together with the filament. Accordingly, we speculate that the tether-weakening reconnection probably destabilized the filament system and triggered its rise. Subsequently, the filament and the sigmoid structure erupted together and produced a coronal mass ejection. After the eruption, the emerging magnetic fields continued to reconnect with the remaining filament channel, leading to the reformation of the filament. This observation strongly supports the idea that emerging magnetic flux plays an important role in triggering the filament to erupt, and the filament is reformed by magnetic reconnection between the emerging magnetic fields and its nearby filament channel.