The suction bucket jacket foundation is widely regarded as a crucial solution for constructing offshore wind farms in water depths ranging from 30 m to 50 m. When subjected to complex loads, the bucket primarily relies on vertical movement to withstand the corresponding loads. This paper investigates the undrained pullout characteristics of the bucket foundation through numerical simulation while keeping its weight constant. This study examined how the pullout capacity of the suction bucket jacket foundation is affected by the aspect ratio and soil conditions. It revealed the changing patterns of bucket–soil frictional resistance and suction during the undrained pullout process, along with their contributions to the pullout capacity of the foundation. The results indicate that the peak pullout load of the bucket increases with decreasing L/D, and the response is more pronounced in soft clay. The frictional resistance changes from upward to downward with increasing displacement, with the maximum frictional resistance occurring at the base of the foundation. The lower part of the footing has a faster response. The suction force increases with displacement, and the proportion of suction force to peak pullout tends to increase as L/D decreases. The soil failure displacement corresponding to the occurrence of the peak pullout load of the foundation lags behind the displacement at which the frictional resistance of the bucket wall stabilizes.