We present spectra of high-redshift supernovae (SNe) that were takenwith the Subaru low resolution optical spectrograph, FOCAS. These SNewere found in SN surveys with Suprime-Cam on Subaru, the CFH12k cameraon the Canada-France-Hawaii Telescope (CFHT), and the Advanced Camerafor Surveys (ACS) on the Hubble Space Telescope (HST). These SN surveysspecifically targeted z>1 Type Ia supernovae (SNe Ia). From thespectra of 39 candidates, we obtain redshifts for 32 candidates andspectroscopically identify 7 active candidates as probable SNe Ia,including one at z=1.35, which is the most distant SN Ia to bespectroscopically confirmed with a ground-based telescope. An additional4 candidates are identified as likely SNe Ia from the spectrophotometricproperties of their host galaxies. Seven candidates are not SNe Ia,either being SNe of another type or active galactic nuclei. When SNe Iaare observed within a week of maximum light, we find that we canspectroscopically identify most of them up to z=1.1. Beyond thisredshift, very few candidates were spectroscopically identified as SNeIa. The current generation of super red-sensitive, fringe-free CCDs willpush this redshift limit higher.