We present rest frame mid-infrared spectroscopy of a sample of 13 submillimeter galaxies , obtained using the Infrared Spectrograph ( IRS ) on board the Spitzer Space Telescope . The sample includes exclusively bright objects from blank fields and cluster lens assisted surveys that have accurate interferometric positions . We find that the majority of spectra are well fitted by a starburst template or by the superposition of PAH emission features and a weak mid-infrared continuum , the latter a tracer of Active Galactic Nuclei ( including Compton-thick ones ) . We obtain mid-infrared spectroscopic redshifts for all nine sources detected with IRS . For three of them the redshifts were previously unknown . The median value of the redshift distribution is z \sim 2.8 if we assume that the four IRS non-detections are at high redshift . The median for the IRS detections alone is z \sim 2.7 . Placing the IRS non-detections at similar redshift would require rest frame mid-IR obscuration larger than is seen in local ULIRGs . The rest frame mid-infrared spectra and mid- to far-infrared spectral energy distributions are consistent with those of local ultraluminous infrared galaxies , but scaled-up further in luminosity . The mid-infrared spectra support the scenario that submillimeter galaxies are sites of extreme star formation , rather than X-ray-obscured AGN , and represent a critical phase in the formation of massive galaxies .