The paper presents the research results obtained in the process of oxidative coupling of methane, in which unpurified biogas was used as the feedstock. Biogas obtained from two kinds of biomass materials, i.e., plant materials (potato and beet pulp, Corn-Cob-Mix—biogas 1) and animal waste (waste from fish filleting—biogas 2) was considered. The influence of temperature, the ratio of methane/oxygen and total flows of feedstock on the catalytic performance in oxidative coupling of methane process was investigated. Comparative tests were carried out using pure methane and a mixture of methane-carbon dioxide to simulate the composition of biogas 2. The process was carried out in the presence of an Mn-Na2WO4/SiO2 catalyst. Fresh and used catalysts were characterised by means of powder X-ray diffraction, X-ray photoelectron spectroscopy, and low-temperature nitrogen adsorption techniques. In oxidative coupling of methane, the type of raw material used as the source of methane has a small effect on methane conversion (the differences in methane conversion are below 3%), but a significant effect on the selectivity to C2. Depending on the type of raw material, the differences in selectivity to C2 reach as high as 9%. However, the Mn-Na2WO4/SiO2 catalyst operated steadily in the tested period of time at any feedstock composition. Moreover, it was found that CO2, which is the second main component of biogas in addition to methane, has an effect on catalytic performance. Comparative results of catalytic tests indicate that the CO2 effect varies with temperature. Below 1073 K, CO2 exerts a small poisoning effect on methane conversion, while above this temperature the negative effect of CO2 disappears. In the case of selectivity to C2+, the negative effect of CO2 was observed only at 1023 K. At higher temperatures, CO2 enhances selectivity to C2+. The effect of CO2 was established by correlating the catalytic results with the temperature programmed desorption of CO2 investigation. The poisoning effect of CO2 was connected with the formation of surface Na2CO3, whose concentration depends on temperature.