Involved in the biosynthesis of mycocyclosin. It uses activated amino acids in the form of aminoacyl-tRNAs (aa-tRNAs) as substrates to catalyze the ATP-independent formation of cyclodipeptides which are intermediates in diketopiperazine (DKP) biosynthetic pathways. Catalyzes the formation of cyclo(L-Tyr-L-Tyr) (cYY) from L-tyrosyl-tRNA(Tyr). Can incorporate various nonpolar residues, such as L-phenylalanine, L-leucine, L-tyrosine and L-methionine, and to a much lesser extent L-alanine, into cyclodipeptides. Cyclodipeptides synthesized by Rv2275 always contain L-tyrosine. 2 L-tyrosyl-tRNA(Tyr) = cyclo(L-tyrosyl-L-tyrosyl) + 2 tRNA(Tyr) Homodimer. The reaction proceeds following a ping-pong mechanism forming a covalent intermediate between an active site Ser-88 and the L-phenylalanine residue. Belongs to the CDPS family.