Grass collected as part of roadside maintenance is conventionally subjected to composting, which has the disadvantage of generating significant CO2 emissions. Thus, it is crucial to find an alternative method for the utilisation of grass waste. The aim of this study was to determine the specific biogas yield (SBY) from the anaerobic mono-digestion of grass from road verges and to assess the content of Fatty Acid Methyl Esters (FAMEs) in grass in relation to the time of cutting and the preservation method of the studied material. The biochemical biogas potential (BBP) test and the FAMEs content were performed on fresh and ensiled grass collected in spring, summer, and autumn. The highest biogas production was obtained from fresh grass cut in spring (715.05 ± 26.43 NL kgVS−1), while the minimum SBY was observed for fresh grass cut in summer (540.19 ± 24.32 NL kgVS−1). The methane (CH4) content in the biogas ranged between 55.0 ± 2.0% and 60.0 ± 1.0%. The contents of ammonia (NH3) and hydrogen sulphide (H2S) in biogas remained below the threshold values for these inhibitors. The highest level of total FAMEs was determined in fresh grass cut in autumn (98.08 ± 19.25 mg gDM−1), while the lowest level was detected in fresh grass cut in spring (56.37 ± 7.03 mg gDM−1). C16:0 and C18:0, which are ideal for biofuel production, were present in the largest amount (66.87 ± 15.56 mg gDM−1) in fresh grass cut in autumn. The ensiling process significantly impacted the content of total FAMEs in spring grass, leading to a reduction in total saturated fatty acids (SFAs) and an increase in total unsaturated fatty acids (USFAs). We conclude that grass biomass collected during the maintenance of road verges is a valuable feedstock for the production of both liquid and gaseous biofuels; however, generating energy from biogas appears to be more efficient than producing biodiesel.