A low noise (1{sigma}rms~3mK) 1mm spectral survey (214.5-285.5GHz) of the oxygen-rich supergiant VY Canis Majoris and the carbon-rich asymptotic giant branch star IRC +10216 has been conducted using the Arizona Radio Observatory's 10m Submillimeter Telescope. Here the complete data set is presented. This study, carried out with a new ALMA-type receiver, marks the first continuous band scan of an O-rich circumstellar envelope, and the most sensitive survey to date of IRC+10216. In VY CMa, 130 distinct molecular lines were detected, 14 of which cannot be identified; in IRC +10216, 717 lines were observed, with 126 features remaining unidentified. In the 1mm bands of VY CMa and IRC +10216, emission is present from 18 and 32 different chemical compounds, respectively, with 10 species common to both sources. Many narrow emission lines were observed in both circumstellar shells, arising from vibrationally excited molecules and from refractory-containing species. Line profiles in VY CMa also exhibit a variety of different shapes, caused by the complex, asymmetric outflow of this object.