We report the results of a multiscale study aimed at understanding cosmic dust evolution under X-ray irradiation. This study combines results from (i) laboratory experiments on cosmic dust analogs, (ii) a model of X-ray secondary ionization processes at the atomic scale, and (iii) an astrophysical model describing dust evolution in protoplanetary disks. Polyaromatic carbon grains were generated in the COSmIC facility at NASA Ames using an argon supersonic free jet expansion (<200 K) seeded with single-ring aromatic molecules (benzene (C6H6), pyridine (C6H5N), and phenol (C6H6O)) and exposed to a high voltage plasma discharge. Crystalline silicate (enstatite, MgSiO3) grains were prepared at MPIA Jena via melting-quenching and laser ablation followed by thermal annealing. We performed controlled X-ray irradiation sequences on these samples using synchrotron soft X-rays at 285 and 970 eV on the carbon grains and 500 eV X-rays on the silicate grains. Infrared 3.4 µm band absorption spectra of the irradiated carbon samples revealed ~80% band intensity loss, for a dose ~5×1023 eV cm-2. Infrared 10 µm band spectra of the irradiated silicates revealed loss of ~95% of the original band intensity in addition to amorphization indicated by FWHM broadening of the individual Gaussian components. To model the apparent mass loss, we employed a hybrid Monte Carlo particle trajectory approach where samples are approximated as atomistic ensembles. As a result of X-ray ionization and ensuing Coulomb explosions on surface molecules, the calculated mass loss is ~45% for the carbon and silicate samples, within a factor of 2 of the infrared band intensity loss. We use these laboratory X-ray destruction rates to estimate the lifetimes of silicate and carbon dust grains in protoplanetary disks. These models show that although destruction timescales are short (a few Myr) at the disk surface, they are longer than typical disk lifetimes (>10 Myr) over the bulk of the disk.