To establish the microscopic P-T phase diagram of recent 112-type iron-pnictides Eu(Fe1-xNix)As2 (x = 0, 0.04), high-pressure synchrotron Mössbauer spectroscopy experiments in Eu151 and Fe57 have been performed. In EuFeAs2 application of pressure completely suppresses the itinerant electron magnetism from the Fe sublattice and the local-moment magnetism in Eu ions at ∼10 and ∼11.6GPa, respectively. High-pressure x-ray diffraction experiments in EuFeAs2 reveal an anomalous change in the lattice parameters and a discontinuity in volume around 10 GPa, suggesting an isostructural transition at this pressure. With Ni-doping (x = 0.04), a collapse of local magnetic order occurs at ∼8GPa, a lower critical pressure compared with the parent compound. In both systems, the suppression of local-moment magnetism is associated with a significant increase of mean valence in Eu ions.