In order to study the behavior of molten blast furnace slag ligament breakup into droplets by centrifugal granulation with a spinning cup, three-dimensional transient CFD model simulations were performed in the present work to study the process of the slag deformation into ligaments upon leaving the spinning cup, which eventually disintegrate into droplets. The formation of molten slag ligaments at the edge of the spinning cup and their disintegration into droplets were numerically revealed so that the behavior and mechanism of the slag ligament breakup into droplets could be investigated. This work specifically examined the influence of cup spinning speed on the diameter and length of the molten slag ligaments around the cup periphery and the diameter of the droplets produced. The simulation results show that, for the same slag flowrate, with the increase in cup spinning speed, the slag film thickness at the cup edge decreases, the number of molten slag ligaments increases, and the diameter of the ligaments decreases, thus reducing the diameter of slag droplets. Moreover, as the number of molten slag ligaments increases as a result of the increased cup spinning speed, the flowrate of a single ligament decreases, so that the ligament disintegrates in a shorter radial distance, that is, the length of the ligament is shortened. In addition, this work also investigated the behavior and mechanism of a single molten slag ligament breakup into droplets. It was found that the process of molten slag ligament breakup into droplets under the action of centrifugal force and surface tension can also be approximately explained by the theory of the Rayleigh disintegration mechanism.