A series of monometallic platinum and bimetallic platinum−rhenium catalysts supported on mesoporous carbon Sibunit, which is a type of mesoporous, microcrystalline carbon, were investigated for hydrodeoxygenation (HDO) of isoeugenol (IE) at 200−300 °C and 30 bar of H2, using dodecane as a solvent. Catalytic activity was tested in a batch reactor to screen the catalysts and, for comparison, also in the continuous mode. For batch experiments, complete conversion, and a high yield of the desired product, propylcyclohexane (PCH), were obtained for all bimetallic PtRe/Sibunit in 240 min, with the highest yield of PCH when Pt:Re ratio was 1:1 or 1:3. The results for Pt−Re (1:1) were reproducible, in terms of catalytic activity and reusability of catalysts, which showed no deactivation. Monometallic Pt catalysts displayed low activity. Continuous experiments were performed with PtRe(1:1)/Sibunit at 30 bar H2, 0.5 mL/min of the liquid flow, and temperatures between 75 °C and 200 °C. The distribution of products showed deoxygenation at higher temperatures, while at lower temperatures, mainly oxygenated products were formed. XPS results confirmed the presence of ReOx species, where an increase in the platinum loading resulted in a decrease in the fraction of ReOx species and subsequently lower PCH yield.