Ball-milled hydroreactive powders of Mg-Al scrap with 20 wt.% additive (Wood’s alloy, KCl, and their mixture) and with no additives were manufactured. Their hydrogen yields and reaction rates in a 3.5 wt.% NaCl aqueous solution at 15–35 °C were compared. In the beginning of the reaction, samples with KCl (20 wt.%) and Wood’s alloy (10 wt.%) with KCl (10 wt.%) provided the highest and second-highest reaction rates, respectively. However, their hydrogen yields after 4 h were correspondingly the lowest and second-lowest percentages—(45.6 ± 4.4)% and (56.0 ± 1.2)% at 35 °C. At the same temperature, samples with 20 wt.% Wood’s alloy and with no additives demonstrated the highest hydrogen yields of (73.5 ± 10.0)% and (70.6 ± 2.5)%, correspondingly, while their respective maximum reaction rates were the lowest and second-lowest. The variations in reaction kinetics for the powders can be explained by the difference in their particle sizes (apparently affecting specific surface area), the crystal lattice defects accumulated during ball milling, favoring pitting corrosion, the morphology of the solid reaction product covering the particles, and the contradicting effects from the potential formation of reaction-enhancing microgalvanic cells intended to induce anodic dissolution of Mg in conductive media and reaction-hindering crystal-grain-screening compounds of the alloy and metal scrap components.