We have performed a spectroscopic study of seven Type 2 QSOs using the mid-infrared spectrometer IRS on board the Spitzer Space Telescope. These are (to our knowledge) the first mid-IR spectra of X-ray-selected QSO2s taken. The objects have been selected according to their high intrinsic luminosities and column densities in X-rays. Their spectra strongly differ from template spectra of Type 2 active galactic nuclei (AGNs) at lower luminosities. They do not exhibit strong PAH dust emission features from circumnuclear star-forming regions, typical for lower luminosity Type 2 Seyfert galaxies or other previously used QSO2 templates, such as the (ultra)luminous infrared galaxy ([U]LIRG) NGC 6240. They also do not show the ice and silicate absorption features of highly luminous but deeply embedded compact nuclei seen in some ULIRGs. Instead, they reveal a relatively featureless, rising continuum similar to luminous Type 1 AGNs. We also find evidence for a 10 μm silicate feature in emission. Models of dusty tori in the AGN unification scenario predict this only for Type 1 AGNs. The ratio of the AGN continuum luminosity at 6 μm to the absorption-corrected 2-10 keV X-ray AGN luminosity is very similar to that found in Seyfert galaxies. X-ray-selected QSO2s are thus characterized by powerful AGNs in hosts with a luminosity due to star formation 1011 L☉. The dominance of the AGN light in the mid-IR spectra of QSO2s together with their flatter spectral energy distributions (SEDs) places important constraints on models of the cosmic infrared background and of the star formation history of the universe.