Using a pump-probe technique, the reactions of Mg(4 S-1(0) and 3 D-1(2)) with H-2 have been measured to yield similar rotational distributions of MgH(v=0 and 1) as that obtained for the reaction of the Mg(3 P-1(1)) state with H-2. A series of measurements is conducted to clarify that the reactions are initiated directly by these higher states, rather than occurring from the lower 3 P-1(1) state following radiative and collisional relaxation. The reactivity of the Mg 4 S-1(0) state with H-2 is found to be comparable to that of the 3 P-1(1) state, but about three times larger than that of the 3 D-1(2) state. The Mg(4 S-1(0), 3 D-1(2))-H-2 reactions proceed via a harpoon-type process, and are closely associated with the Mg(3 P-1(1))-H-2 reaction coordinate through evolution of a series of surface crossings. To support our suggestion that the harpoon mechanism is involved, the cross sections of collisional deactivation by H-2 for various excited states are measured. The ratios of cross sections observed for the 3 P-1(1), 4 S-1(0), and 5 S-1(0) state, equal to 1:2.85:4.3, are consistent with the calculated prediction of 1:2.62:4.24. The calculated cross sections are based on a simple hard sphere model with effective radii evaluated differently. Here, the effective radii for the higher states are determined from the crossing of ionic and covalent curves, while the Mg(3 P-1(1))-H-2 radius is estimated from the nonadiabatic crossing between the reactive 1 B-1(2) state and the ground state. Consistency between observation and prediction confirms that the harpoon mechanism proposed in this work is plausible.