Using the Infrared Spectrograph (IRS) on board the Spitzer Space Telescope, we have obtained rest frame mid-infrared spectroscopy of two bright submillimeter galaxies. SMMJ02399-0136 at z=2.81 shows a superposition of PAH emission features and a mid-infrared continuum, indicating significant and roughly equal contributions to its bolometric luminosity from star formation and from a Compton-thick AGN. We derive a new redshift of z=2.80 for MMJ154127+6616 from the IRS spectrum and find this object is dominated by starburst PAH emission. The rest frame mid- to far-infrared spectral energy distributions are consistent with these submillimeter galaxies being scaled u