Catalyzes the dephosphorylation of diacylglycerol phosphate (DGPP) to phosphatidate (PA) and the subsequent dephosphorylation of PA to diacylglycerol (DAG). a 1,2-diacyl-sn-glycerol 3-diphosphate + H2O = a 1,2-diacyl-sn-glycero-3-phosphate + H(+) + phosphate a 1,2-diacyl-sn-glycero-3-phosphate + H2O = a 1,2-diacyl-sn-glycerol + phosphate Belongs to the PA-phosphatase related phosphoesterase family.