A novel method based on a Na2S2O8/urea composite system was used to both synchronously absorb SO2 and NO from marine diesel engine emissions and reduce the nitrate residues in cleaning wastewater. In the Na2S2O8/urea solution, a temperature of over 60 °C and a Na2S2O8 concentration of >0.05 mol/L were found to fully absorb SO2 by overcoming the SO2 release and effectively absorb NO. Urea successfully reduced the residual nitrate concentration and improves NO absorption at a concentration below 2 mol/L. The NO and SO2 removal efficiencies reached 97.8 ± 1.5% and 100%, respectively, at 70 °C in 0.1 mol/L Na2S2O8 and 1.5 mol/L urea solutions. The residual nitrate concentration was 8.12 ± 0.25 mg/L, far below the regulatory limit of 60 mg/L. Acidic conditions (pH ≤ 5.5) could be conducive to absorbing NO and reducing the residual nitrate concentration. Based on the experimental results, this novel method is highly promising for reducing ship emissions.