In this work, we focus on the study of the structural and elastic properties of mercury digallium selenide (HgGa₂Se₄) which belongs to the family of AB₂X₄ ordered-vacancy compounds with tetragonal defect chalcopyrite structure. We have carried out high-pressure x-ray diffraction measurements up to 13.2 GPa. Our measurements have been complemented and compared with total-energy ab initio calculations. The equation of state and the axial compressibilities for the low-pressure phase of HgGa₂Se₄ have been experimentally and theoretically determined and compared to other related ordered-vacancy compounds. The theoretical cation-anion and vacancy-anion distances in HgGa₂Se ₄ have been determined. The internal distance compressibility in HgGa₂Se₄ has been compared with those that occur in binary HgSe and ε-GaSe compounds. It has been found that the Hg-Se and Ga-Se bonds behave in a similar way in the three compounds. It has also been found that bulk compressibility of the compounds decreases following the sequence "ε-GaSe > HgGa₂Se₄ > HgSe." Finally, we have studied the pressure dependence of the theoretical elastic constants and elastic moduli of HgGa₂Se₄. Our calculations report that the low-pressure phase of HgGa₂Se₄ becomes mechanically unstable above 13.3 GPa.