Has 3'-5' poly(A) exoribonuclease activity for synthetic poly(A) RNA substrate. Its function seems to be partially redundant with that of CNOT8. Catalytic component of the CCR4-NOT complex which is one of the major cellular mRNA deadenylases and is linked to various cellular processes including bulk mRNA degradation, miRNA-mediated repression, translational repression during translational initiation and general transcription regulation. During miRNA-mediated repression the complex seems also to act as translational repressor during translational initiation. Additional complex functions may be a consequence of its influence on mRNA expression. Associates with members of the BTG family such as TOB1 and BTG2 and is required for their anti-proliferative activity. Exonucleolytic cleavage of poly(A) to 5'-AMP. Binds 2 divalent metal cations per subunit with RNAase activity being higher in presence of Mn(2+) than of Mg(2+) or Co(2+). Component of the CCR4-NOT complex; distinct complexes seem to exist that differ in the participation of probably mutually exclusive catalytic subunits; the complex contains two deadenylase subunits, CNOT6 or CNOT6L, and CNOT7 or CNOT8 (PubMed:19558367). In the complex, interacts directly with CNOT1 (PubMed:21336257). Interacts with AGO2 (By similarity). Interacts with TOB1; recruited by TOB1 to a ternary complex with CPEB3 which is required for mRNA deadenylation and decay (PubMed:21336257, PubMed:23236473, PubMed:19276069). Interacts with BTG1 (By similarity). Interacts with BTG2 (PubMed:23236473). Interacts with NANOS2 (By similarity). Interacts with ZFP36, ZFP36L1 and ZFP36L2; these interactions are inhibited in response to phorbol 12-myristate 13-acetate (PMA) treatment in a p38 MAPK-dependent manner (PubMed:25106868). Interacts with TARDBP (PubMed:30520513). Interacts with BTG4 (PubMed:32502391). Interacts with EIF4E; this interaction is increased by CNOT7 interaction with BTG4 (By similarity). NANOS2 promotes its localization to P-body. Belongs to the CAF1 family.