We present the results of spectroscopic observations from the ESSENCE high-redshift supernova (SN) survey during its first four years of operation. This sample includes spectra of all SNe Ia whose light curves were presented by Miknaitis et al. and used in the cosmological analyses of Davis et al. and Wood-Vasey et al. The sample represents 273 hr of spectroscopic observations with 6.5-10 m class telescopes of objects detected and selected for spectroscopy by the ESSENCE team. We present 184 spectra of 156 objects. Combining this sample with that of Matheson et al., we have a total sample of 329 spectra of 274 objects. From this, we are able to spectroscopically classify 118 Type Ia SNe. As the survey has matured, the efficiency of classifying SNe Ia has remained constant while we have observed both higher-redshift SNe Ia and SNe Ia farther from maximum brightness. Examining the subsample of SNe Ia with host-galaxy redshifts shows that redshifts derived from only the SN Ia spectra are consistent with redshifts found from host-galaxy spectra. Moreover, the phases derived from only the SN Ia spectra are consistent with those derived from light-curve fits. By comparing our spectra to local templates, we find that the rate of objects similar to the overluminous SN 1991T and the underluminous SN 1991bg in our sample are consistent with that of the local sample. We do note, however, that we detect no object spectroscopically or photometrically similar to SN 1991bg. Although systematic effects could reduce the high-redshift rate we expect based on the low-redshift surveys, it is possible that SN 1991bg-like SNe Ia are less prevalent at high redshift.