The fate of biobased and biodegradable cellulose-derived plastics in landfills represents an important topic from economic and environmental points of view. Anaerobic digestion is a cost-effective waste-to-energy technology. The behaviour of six polymer types—that is, cellulose (C), cellulose acetate (CA), viscose (V), nanocellulose (NC), acetate textile (AT), and heteropolysaccharide pectin (P)—was studied under anaerobic batch mesophilic conditions in a landfill leachate for 147 days. The cumulative biogas production was as follows: C>V=CA>>AT>>NC=P. Metagenomic analysis revealed notable variations in the proportion of bacterial and archaeal domains with the highest archaeal abundance in the presence of CA (80.2%) and C (78.5%). At the end of digestion, cellulolytic, hydrolytic, and dehydrogenase activities were measured in the intact samples, as well as the liquid and solid fractions, under aerobic and anaerobic conditions. Cellulolytic activity in P was detected only in the pellet, while in NC, activity was mostly in the supernatant under both aerobic and anaerobic conditions. Scanning electron microscopy and confocal scanning laser microscopy showed a defragmentation and degradation of polymeric substrates as well as microbial colonisation. Based on the results, landfill leachate is appropriate for the anaerobic biodegradation of cellulose-derived polymers; however, the process is polymer specific.