Response surface methodology (RSM) was used to find the optimal extraction process of Oudemansiella raphanipies polysaccharides (ORPs). The results showed that the optimal extraction parameters were an alkali concentration of 0.02 mol/L, a ratio of material to liquid of 1:112.7 g/mL, an extraction temperature of 66.0 °C, and an extraction time of 4.0 h. Under the optimal conditions, the yield of ORPs was raised to 16.2 ± 0.1%. The antioxidant activities of ORPs-I~V were determined and compared, and ORPs-V was further purified by chromatography, with an average molecular weight (Mw) of 18.86 kDa. The structure of ORPs-V was determined by Fourier transform-infrared spectroscopy (FT-IR), monosaccharide analysis, and nuclear magnetic resonance (NMR) spectroscopy. The ORPs-V comprised fucose, rhamnose, arabinose, glucose, galactose, mannose, xylose, fructose, galacturonic acid, and glucuronic acid at a ratio of 1.73:1.20:1.13:2.87:8.71:2.89:1.42:0.81. Compared to other ORPs, ORPs-V showed the strongest antioxidant activities (ABTS radical cation, hydroxyl radical and DPPH scavenging activities, and reducing power), and were able to significantly increase the activities of superoxide dismutase, catalase, lactate dehydrogenase, and glutathione peroxidase. However, they reduced the malondialdehyde content in mice fed a high-fat diet. These results indicate that ORPs-V may be good anti-oxidant agents to be applied in functional foods.