The core-ionization spectra of mixed Be-Mg clusters are computed by accurate ab initio methods. They are found to exhibit a variety of strong and unexpected effects originating from the presence of neighboring atoms of the same (native) or the other (foreign) element. The spectra reveal unusually low-lying intense satellites and the band shapes are sensitive to the local environment of the core-ionized atom. Foreign and native screening processes compete with each other resulting in specific spectral features which uniquely characterize the clusters.