Using synchrotron X-ray diffraction and diamond anvil cells we performed in situ high-pressure studies of mullite-type phases of general formula Al4+2xSi22xO10x and differing in the amount of oxygen vacancies: 2:1-mullite (x=0.4), 3:2-mullite (x=0.25), and sillimanite (x=0). The structural stability of 2:1-mullite, 3:2-mullite, and sillimanite was investigated up to 40.8, 27.3, and 44.6GPa, respectively, in quasi-hydrostatic conditions, at ambient temperature. This is the first report of a static high-pressure investigation of Al2O3SiO2 mullites. It was found that oxygen vacancies play a significant role in the compression mechanisms of the mullites by decreasing the mechanical stability of the phases with the number of vacancies. Elevated pressure leads to an irreversible amorphization above similar to 20GPa for 2:1-mullite and above 22GPa for 3:2-mullite. In sillimanite, only a partial amorphization is observed above 30GPa. Based on Rietveld structural refinements of high-pressure X-ray diffraction patterns, the pressure-driven evolution of unit cell parameters is presented. The experimental bulk moduli obtained are as follows: K0 = 162(7)GPa with K0 = 2.2(6) for 2:1-mullite, K0 = 173(7)GPa with K0 = 2.3(2) for 3:2-mullite, K0 = 167(7)GPa with K0 = 2.1(4) for sillimanite.