Core-level x-ray photoemission spectra for the Mott-Hubbard systems are calculated by the dynamical mean-field theory based on the exact diagonalization method. The spectra show a two-peak structure, screened and unscreened peaks. The screened peak is absent in a Mott insulator, but develops into the main peak when the correlation strength becomes weak and the system turns metallic. The calculated spectral behavior is consistent with the experimental Ru 3d core-level spectra of various ruthenates. This new mechanism of the core-level photoemission satellite can be utilized to reveal the Mott transition phenomenon in various strongly correlated electron systems, especially in nanoscale devices and phase-separated materials.