We present spectra of high-redshift supernovae (SNe) that were taken with the Subaru low resolution optical spectrograph, FOCAS. These SNe were found in SN surveys with Suprime-Cam on Subaru, the CFH12k camera on the Canada-France-Hawaii Telescope (CFHT), and the Advanced Camera for Surveys (ACS) on the Hubble Space Telescope (HST). These SN surveys specifically targeted z>1 Type Ia supernovae (SNe Ia). From the spectra of 39 candidates, we obtain redshifts for 32 candidates and spectroscopically identify 7 active candidates as probable SNe Ia, including one at z=1.35, which is the most distant SN Ia to be spectroscopically confirmed with a ground-based telescope. An additional 4 candidates are identified as likely SNe Ia from the spectrophotometric properties of their host galaxies. Seven candidates are not SNe Ia, either being SNe of another type or active galactic nuclei. When SNe Ia are observed within a week of maximum light, we find that we can spectroscopically identify most of them up to z=1.1. Beyond this redshift, very few candidates were spectroscopically identified as SNe Ia. The current generation of super red-sensitive, fringe-free CCDs will push this redshift limit higher.