Polarized Raman spectroscopy and single-crystal synchrotron X-ray diffraction were applied to three representative zircon samples exhibiting a negligible, intermediate, and high degree of radiation damage to analyze the pressure-induced structural response up to 10 GPa. It is shown that pressure does not change the overall amorphous fraction, but induces atomic rearrangements at pressures of ~ 2.5 and ~ 6.5 GPa. The first threshold pressure is related to weakening of the Si–O bonds in the amorphous matrix. The second threshold pressure marks the correlated response of the coexisting amorphous and crystalline nanoregions, namely, the beginning of irreversible densification of the amorphous material and reduction of inhomogeneity of radiation-induced strain in the crystallites. The latter process occurs abruptly in the crystalline regions of moderately metamict zircon (amorphous fraction ~ 54%) and more smoothly for heavily metamict zircon (amorphous fraction ~ 84%) due to the different pathways of release of the local strains. The dynamic and static compressibilities as well as the isotropic and anisotropic Grüneisen parameters are considered in detail. The radiation damage increases the volume compressibility of the crystalline fraction as well as the crystal phonon compressibilities and decreases the Grüneisen parameters.