The ferro-liquid droplet manipulation on hydrophobic surfaces remains vital for various applications in biomedicine, sensors and actuators, and oil-water separation. The magnetic influence of ferro-liquid droplets on the hydrophobic surface is elucidated. The mechanisms of a newborn droplet formation under the magnetic force are explored. The sliding and rolling dynamics of the ferro-liquid droplets are assessed for the various concentrations wt % of ferro-particles. High-speed recording and a tracker program are used to evaluate the droplet sliding and translational velocities. It is demonstrated that the mode of droplet motion changes from sliding to rolling as the magnetic Bond number increases, in which case, the droplet position becomes close to the magnet surface. The translational velocity of the droplet under rolling mode increases as the ferro-particle concentration in the droplet fluid increases. A further increase of the magnetic Bond number results in the creation of a newborn droplet attached to the magnet surface.