The reactive adsorption desulfurization (RADS) of a model spent tire pyrolysis oil, using n-hexane as the hydrocarbon fuel and thiophene as the sulfur-bearing compound, over a co-precipitated nickel-molybdenum (Ni-Mo) adsorbent was examined. The percentage of sulfur removal, indicating the efficacy of the adsorbent, was evaluated in a continuous fixed-bed reactor operating over a range of conditions including reaction time (1–10 h), temperature (250–300 °C), pressure (0.2–1 MPa), and hydrogen to sulfur (H:S) molar ratio (14–108). The fresh, reduced, and spent adsorbents were characterized by elemental analyzer and ICP-OES for the element contents, BET for the surface area and pore properties, SEM for the morphology, STEM-EDS for the element distributions, and XRD for the change of Ni, Mo, and S mineral phases in the adsorbent with the change of reaction time. The Ni-Mo adsorbent achieved a high percentage of sulfur removal of 99.9 wt% under mild reaction conditions of 300 °C, 1 MPa, and 108 H:S molar ratio. The corresponding breakthrough sulfur capacity of the adsorbent was 288 mg g−1. Increasing reaction temperature, pressure, or H:S molar ratio led to a greater percentage of sulfur removal. Ni and Mo played cooperative and multifunctional roles in the RADS process, firstly as sulfur acceptors, then as active centers for hydrodesulfurization (HDS). The Ni and MoS2 phases formed during the RADS process functioned as highly effective HDS catalyst cycles, which improved the sulfur transfer rate and facilitated the continuation of sulfur removal.