We present the results of XMM-Newton X-ray observations of the Mira AB binary system, which consists of a pulsating, asymptotic giant branch primary and nearby (~0.6 separation) secondary of uncertain nature. The EPIC CCD (MOS and pn) X-ray spectra of Mira AB are relatively soft, peaking at ~1 keV, with only very weak emission at energies > 3 keV; lines of Ne IX, Ne X, and O VIII are apparent. Spectral modeling indicates a characteristic temperature T_X ~ 10^7 K and intrinsic luminosity L_X ~ 5x10^29 erg s^{-1}, and suggests enhanced abundances of O and, possibly, Ne and Si in the X-ray-emitting plasma. Overall, the X-ray spectrum and luminosity of the Mira AB system more closely resemble those of late-type, pre-main sequence stars or late-type, magnetically active main sequence stars than those of accreting white dwarfs. We conclude that Mira B is most likely a late-type, magnetically active, main-sequence dwarf, and that X-rays from the Mira AB system arise either from magnetospheric accretion of wind material from Mira A onto Mira B, or from coronal activity associated with Mira B itself, as a consequence of accretion-driven spin-up. One (or both) of these mechanisms also could be responsible for the recently discovered, point-like X-ray sources within planetary nebulae.
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