The pressure dependence of the superconducting transition temperature Tc, the local structure, and the electronic properties of the iron chalcogenide superconductor FeSe_0.5Te_0.5 was investigated by means of SQUID magnetometry and site-selective polarized x-ray absorption spectroscopy at the iron and selenium K-edges. The measurements reveal a discontinuous decrease of the local bond distances by crossing a tetragonal to monoclinic structural phase transition at p_S∼2.7 GPa. The electronic structure, however, evolves evenly, but the superconducting properties are highly affected by changes in the local structure. These results underline the close connection of the lattice and the superconductivity in the iron-based superconductors.