Metallocarboxypeptidase that mediates deglutamylation of tubulin and non-tubulin target proteins. 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. Cleaves alpha- and gamma-linked polyglutamate tubulin side-chain, as well as the branching point glutamate. Also catalyzes the removal of alpha-linked glutamate residues from the carboxy-terminus of alpha-tubulin. gamma-L-glutamyl-L-glutamyl-[protein] + H2O = L-glutamate + L-glutamyl-[protein] (L-glutamyl)(n+1)-gamma-L-glutamyl-L-glutamyl-[protein] + H2O = (L-glutamyl)(n)-gamma-L-glutamyl-L-glutamyl-[protein] + L-glutamate C-terminal L-alpha-aminoacyl-L-glutamyl-[tubulin] + H2O = C-terminal L-alpha-aminoacyl-[tubulin] + L-glutamate C-terminal L-alpha-aminoacyl-L-glutamyl-L-glutamyl-[tubulin] + H2O = C-terminal L-alpha-aminoacyl-L-glutamyl-[tubulin] + L-glutamate Binds 1 zinc ion per subunit. Belongs to the peptidase M14 family.