Due to the simple layered structure, isostructural FeSe and FeSe_0.5Te_0.5 are clue compounds for understanding the principal mechanisms of superconductivity in the family of Fe-based superconductors. High-pressure magnetic, structural and Mössbauer studies have been performed on single-crystalline samples of superconducting FeSe_0.5Te_0.5 with T_c = 13.5 K. Susceptibility data have revealed a strong increase of T_c up to 19.5 K for pressures up to 1.3 GPa, followed by a plateau in the T_c(p) dependence up to 5.0 GPa. Further pressure increase leads to a disappearance of the superconducting state around 7.0 GPa. X-ray diffraction and Mössbauer studies explain this fact by a tetragonal-to-hexagonal structural phase transition. Mössbauer parameters of the non-superconducting high-pressure phase indicate less covalency of FeSe bonds. Based on structural and susceptibility data, we conclude about a common character of T_c(p) diagrams for both FeSe and FeSe_0.5Te_0.5 superconductors.