Abstract: In this paper, the complex physical phenomenon of metal droplets impacting a pool of the same liquid under the action of an external vertical magnetic field is investigated in depth by means of numerical simulations. The study is carried out in an axisymmetric coordinate system, and in order to solve the Navier-Stokes (N-S) equations with the Lorentz force term accurately, the modified volume of fluid (VOF) method and adaptive mesh refinement technique are employed to treat the Lorentz force as an external volume force, which effectively improves the accuracy and computational efficiency of the numerical simulation. Under different Reynolds numbers (ranging from 700 to 13000) and Weber numbers (ranging from 40 to 520), the droplet impact phenomenon is carefully categorized into three types based on the evolution of vortex states: no vortex detachment, vortex detachment, and formation of von Karmen vortex street. The results show that in the case of no vortex shedding, the sputtering phenomenon can be significantly suppressed by increasing the magnetic field strength or the surface tension. In the case of vortex shedding and Von Karmen vortex street formation, the surface tension mainly inhibits the sputtering process, while the vertical magnetic field affects the structure of the vortex ring, resulting in a change in the morphology and distribution of the vortex ring, and slows down the outward motion of the sputtering jet, which changes the dynamics of the droplet field after impact. In particular, when a continuous vortex shedding process triggers the formation of a von Karmen vortex street, the first generated jet oscillates in its root region, and the frequency of the oscillation is closely related to the vortex shedding phenomenon of the von Karmen vortex street. Further analysis reveals that the vertical magnetic field has a non-monotonic influence on the initial oscillating behavior of the jet, which provides a key theoretical basis for a deeper understanding of the complex flow mechanisms during droplet impact in a magnetohydrodynamic environment.