Maintenance of urban green infrastructure generates a large amount of biomass that can be considered a valuable feedstock for biogas production. This study aims to determine the effect of the cutting time and method of substrate preservation on the specific methane yield (SMY) of urban grass collected from road verges and median strips between roadways in wet (WF) and dry fermentation (DF) technology. The grass was collected three times in a growing season, including in spring, summer, and autumn. The biochemical methane potential (BMP) test was performed on fresh grass, grass ensiled without additives, and grass ensiled with microbiological additives. In addition, the energy potentially produced from biogas and the avoided CO2 emissions were calculated. The highest SMY (274.18 ± 22.59 NL kgVS−1) was observed for the fresh grass collected in spring and subjected to WF. At the same time, the lowest CH4 production (182.63 ± 0.48 NL kgVS−1) was found in the grass ensiled without additives, collected in summer, and digested in DF technology. A comparison of the SMY obtained from the same grass samples in the WF and DF technologies revealed that higher CH4 yields were produced in WF. The electricity and heat production were affected by the time of grass cutting, ensilage method, and AD technology. Generally, less electricity but more heat was produced in DF technology. The least electricity (469–548 kWh tDM−1) was produced from the grass cut in spring and subjected to DF, while the most electricity (621–698 kWh tDM−1) was obtained from the grass collected in autumn and subjected to WF. In the case of heat production, the situation was reversed. The least heat (1.4–1.9 GJ tDM−1) was produced by the grass collected in spring and subjected to WF, while the most heat (2.2–2.7 GJ tDM−1) was produced by the grass collected in autumn and subjected to DF. Ensilage decreased the electricity and heat production in almost all the cuttings. The total reduction in CO2 emissions may amount to 2400 kg CO2 per 1 hectare of road verges. This significant reduction demonstrates that the use of grass from roadside verges in biogas plants should be considered a feasible option. Even though urban grass should be considered a co-substrate only, it can be a valuable feedstock that may partially substitute energy crops and reduce the area needed for energy purposes. Our results reveal that biogas production from the grass waste in WF technology is a stable process. The cutting time and preservation method do not affect the AD process. In DF technology, fresh grass, especially from the late growing season used as feedstock, extends the time of biomass decomposition and, therefore, should be avoided in a real-life biogas plant.