We report results of a high-pressure investigation by Raman spectroscopy of a classic relaxor ferroelectric (relaxor) PbMg_1/3Nb_2/3O₃ (PMN), which is considered to be a model system for the understanding of relaxor and relaxor-related materials. The observed pressure-dependent Raman spectra are very unusual, pointing to a relaxor-specific spectral signature. We further show that an external pressure of several GPa, as can be met in thin films, alters fundamentally the structural and polar properties of PMN, suggesting that intrinsic instabilities towards pressure play an important role in the reduction of dielectric properties in relaxor and relaxor-related thin films.