Seismic activity often triggers liquefaction in sandy soils, which coupled with initial vertical tensile loads, poses a significant threat to the stability of suction bucket foundations for floating wind turbines. However, there remains a notable dearth of studies on the dynamic response of these foundations under combined seismic and vertical tensile loads. Therefore, this study developed a numerical method for analyzing the dynamic response of suction bucket foundations in sandy soils under such combined loading conditions. Through numerical simulations across various scenarios, this research investigates the influence of key factors such as seismic intensity, spectral characteristics, as well as the magnitude and direction of tensile loads on the seismic response of suction buckets. The results revealed that the strong earthquake may cause the suction bucket foundation of floating wind turbines to fail due to excessive vertical upward displacement. This can be attributed to that the accumulation of excess pore water pressure reduces the normal effective stress on the outer wall of bucket, and consequently decreases the frictional resistance of bucket-soil interface. Additionally, the above factors significantly influence both the vertical displacement of the suction bucket and the development of pore pressure in the surrounding soil. The findings can provide valuable insights for the seismic safety assessment of suction bucket foundations used in tension-leg floating wind turbines.