In this work, we report on high-pressure Raman scattering measurements in mercury digallium sulfide (HgGa₂S₄) with defect chalcopyrite structure that have been complemented with lattice dynamics ab initio calculations. Our measurements evidence that this semiconductor exhibits a pressure-induced phase transition from the completely ordered defect chalcopyrite structure to a partially disordered defect stannite structure above 18 GPa which is prior to the transition to the completely disordered rocksalt phase above 23 GPa. Furthermore, a completely disordered zincblende phase is observed below 5 GPa after decreasing pressure from 25 GPa. The disordered zincblende phase undergoes a reversible pressure-induced phase transition to the disordered rocksalt phase above 18 GPa. The sequence of phase transitions here reported for HgGa₂S₄ evidence the existence of an intermediate phase with partial cation-vacancy disorder between the ordered defect chalcopyrite and the disordered rocksalt phases and the irreversibility of the pressure-induced order-disorder processes occurring in ordered-vacancy compounds. The pressure dependence of the Raman modes of all phases, except the Raman-inactive disordered rocksalt phase, have been measured and discussed.