X-ray microtomography is a widely applied tool for noninvasive structure investigations. The related detectors are usually based on a scintillator screen for the fast in situ conversion of an X-ray image into an optical image. Spatial resolution of the latter is fundamentally diffraction limited. In this work, we introduce stimulated scintillation emission depletion (SSED) X-ray imaging where, similar to stimulated emission depletion (STED) microscopy, a depletion beam is applied to the scintillator screen to overcome the diffraction limit. The requirements for the X-ray source, the X-ray flux, the scintillator screen, and the STED beam were evaluated. Fundamental spatial resolution limits due to the spread of absorbed X-ray energy were estimated with Monte Carlo simulations. The SSED proof-of-concept experiments demonstrated 1) depletion of X-ray excited scintillation, 2) partial confinement of scintillating regions to sub-diffraction sized volumes, and 3) improvement of the imaging contrast by applying SSED.