Catalytic hydrogenolysis, with high conversion and selectivity, promoted by supported palladium substrates in isopropanol and dioxane at a low H2 pressure (0.5 MPa), is reported for the first time. The catalysts, characterized by using BET isotherms, transmission electron microscopy (TEM), temperature-programmed reduction (TPR), powder X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS), were obtained by coprecipitation and impregnation techniques. The coprecipitation method allows catalysts with a metal–metal or a metal–support interaction to be obtained, which enhances the catalytic performance for both the conversion of glycerol and the selectivity to 1,2-propanediol. Analogous reactions carried out with catalysts prepared by using impregnation are less efficient. A study of the solvent and temperature effect is also presented. The obtained results allow the hydrogenolysis mechanism to be inferred; this involves both the direct replacement of the carbon-bonded OH group by an incoming hydrogen or the formation of hydroxyacetone as an intermediate, which subsequently undergoes a hydrogenation process to give 1,2-propanediol. Finally, catalytic tests on a large-scale reaction at a higher H2 pressure and recycling of the samples were carried out with the better performing catalysts (Pd/CoO and Pd/Fe2O3 prepared by using coprecipitation) to verify possible industrial achievements.