Polyurethane is one of the most versatile and commonly applied polymers in the world. Its properties are strongly dependent on the polyol/isocyanate structures and NCO:OH ratio, among other parameters. Additionally, the polyol structure is affected by the catalyst used for the reaction and production. The catalyst may indirectly affect the curing kinetics and mechanical strength of the PU, due to changes of polyol properties. This work evaluates the effects of two catalysts on the polyol structure and thus the effect of these polyol changes on the curing kinetics and mechanical strength of a PU adhesive. Two polyols were synthetized using the same hydroxyl-containing molecules derived from renewable natural sources, but with different types of catalysts (based on Sn or Li/Ti). The synthesized polyols were separately mixed with diphenylmethane diisocyanate in a 1.1:1 ratio of NCO to OH to form two bio-based PUs. The polyols were investigated by Fourier transform infrared (FTIR) spectroscopy, which showed the occurrence of some changes in the chemical groups of the polyol structure for both catalysts, as well as an influence on the curing kinetics. The mechanical behavior of the PU adhesives was characterized by dynamic mechanical analysis (DMA) and peeling tests. The results show a higher curing rate and higher peeling strength for the PU adhesives obtained using the Sn-based catalyst; both adhesives showed cohesive failure.