Solar filaments often exhibit rotation and deflection during eruptions, which would significantly affect the geoeffectiveness of the corresponding coronal mass ejections (CMEs). Therefore, understanding the mechanisms that lead to such rotation and lateral displacement of filaments is a great concern to space weather forecasting. In this paper, we examine an intriguing filament eruption event observed by the Chinese Hα Solar Explorer and the Solar Dynamics Observatory. The filament, which eventually evolves into a CME, exhibits significant lateral drifting during its rising. Moreover, the orientation of the CME flux rope axis deviates from that of the pre-eruptive filament observed in the source region. To investigate the physical processes behind these observations, we perform a data-constrained magnetohydrodynamic simulation. Many prominent observational features in the eruption are reproduced by our numerical model, including the morphology of the eruptive filament, eruption path, and flare ribbons. The simulation results reveal that the magnetic reconnection between the flux rope leg and neighboring low-lying sheared arcades may be the primary mechanism responsible for the lateral drifting of the filament material. Such a reconnection geometry leads to flux rope footpoint migration and a reconfiguration of its morphology. As a consequence, the filament material hosted in the flux rope drifts laterally, and the CME flux rope deviates from the pre-eruptive filament. This finding underscores the importance of external magnetic reconnection in influencing the orientation of a flux rope axis during eruption.
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