Mitochondrial cardiolipin-specific phospholipase which deacylates de novo synthesized cardiolipin (CL). Part of the remodeling process of cardiolipin, which involves deacylation-reacylation of premature cardiolipin. a cardiolipin + H2O = 1'-[1,2-diacyl-sn-glycero-3-phospho],3'-[1-acyl-sn-glycero-3-phospho]-glycerol + a fatty acid + H(+) Monomer. The HXXXXD motif is essential for acyltransferase activity. Belongs to the peptidase S33 family. ABHD4/ABHD5 subfamily.