Effluent streams originating from swine production can be a major cause of point-source pollution and very dangerous for the surrounding environment. In this work, biogas and biomethane potential of swine-derived effluents were assessed under mesophilic conditions (37 °C) among different production stages (Farrowing, Gestation, Weaners, and Fattening) in order to investigate the suitability of anaerobic digestion as a treatment technology and energy recovery tool. Anaerobic biodegradability and kinetic modeling of the different wastewaters were also evaluated in order to better understand the degradation patterns of each waste stream. The specific methane yields for each substrate wastewater were successfully determined gravimetrically and ranged from 293.9 ± 31.6 mL CH4.gVS added for Gestation, 248.0 ± 246.6 mLCH4.gVS added-1 for Fattening, and 172.4 ± 1.62 mLCH4.gVS added-1 for Weaners. Farrowing wastewater presented no detectable biomethane production in the studied conditions probably due to very low organics content. Anaerobic biodegradability results showed that wastewaters from Gestation (60.28%) had a higher biodegradability index when compared with Fattening (37.96%) and Weaners (45.97%) stages. The Logistic and Gompertz models fitted the experimental results well and may provide valuable knowledge for the treatment of specific swine wastewater streams at different growth stages within a perspective of producing biogas. The results obtained in this work should be encouraging for on-farm energy recovery and anaerobic digestion technology viewed as an important contributor to alleviate the increasing energy demand within the swine industry. However, as indicated by biodegradability data and organics removal percentages, biological treatment does not comprise a complete solution and should be complemented with other treatment methods.