Multi-wavelength flares have routinely been observed from the supermassive black hole, Sagittarius A⋆ (Sgr A⋆), at our Galactic center. The nature of these flares remains largely unclear, despite many theoretical models. We study the statistical properties of the Sgr A⋆ X-ray flares and find that they are consistent with the theoretical prediction of the self-organized criticality system with the spatial dimension S = 3. We suggest that the X-ray flares represent plasmoid ejections driven by magnetic reconnection (similar to solar flares) in the accretion flow onto the black hole. Motivated by the statistical results, we further develop a time-dependent magnetohydrodynamic (MHD) model for the multi-band flares from Sgr A⋆ by analogy with models of solar flares/coronal mass ejections (CMEs). We calculate the X-ray, infrared flare light curves, and the spectra, and find that our model can explain the main features of the flares.