Metallocarboxypeptidase that mediates protein deglutamylation of tubulin and non-tubulin target proteins (PubMed:22170066, PubMed:24022482, PubMed:30420557). Catalyzes the removal of polyglutamate side chains present on the gamma-carboxyl group of glutamate residues within the C-terminal tail of alpha- and beta- tubulin (PubMed:22170066, PubMed:24022482, PubMed:30420557). Specifically cleaves tubulin long-side-chains, while it is not able to remove the branching point glutamate (PubMed:24022482). Also catalyzes the removal of polyglutamate residues from the carboxy-terminus of alpha-tubulin as well as non-tubulin proteins such as MYLK (PubMed:22170066). Involved in KLF4 deglutamylation which promotes KLF4 proteasome-mediated degradation, thereby negatively regulating cell pluripotency maintenance and embryogenesis (PubMed:29593216). {ECO:0000269|PubMed:22170066, ECO:0000269|PubMed:24022482, ECO:0000269|PubMed:29593216, ECO:0000269|PubMed:30420557}. This is the function of AGTPBP1 (ATP/GTP binding carboxypeptidase 1, ENSG00000135049).