We report the results from a spectrophotometric study sampling the 300 candidate supernova remnants (SNRs) in M83 identified through optical imaging with Magellan/IMACS and Hubble Space Telescope/WFC3. Of the 118 candidates identified based on a high [SII]{lambda}{lambda}6716,6731 to H{alpha} emission ratio, 117 show spectroscopic signatures of shock-heated gas, confirming them as SNRs-the largest uniform set of SNR spectra for any galaxy. Spectra of 22 objects with a high [OIII]{lambda}5007 to H{alpha} emission ratio, selected in an attempt to identify young ejecta-dominated SNRs like Cas A, reveal only one (previously reported) object with the broad (1000km/s) emission lines characteristic of ejecta-dominated SNRs, beyond the known SN1957D remnant. The other 20 [OIII]-selected candidates include planetary nebulae, compact HII regions, and one background QSO. Although our spectroscopic sample includes 22 SNRs smaller than 11pc, none of the other objects show broad emission lines; instead their spectra stem from relatively slow (~200km/s) radiative shocks propagating into the metal-rich interstellar medium of M83. With six SNe in the past century, one might expect more of M83's small-diameter SNRs to show evidence of ejecta; this appears not to be the case. We attribute their absence to several factors, including that SNRs expanding into a dense medium evolve quickly to the ISM-dominated phase, and that SNRs expanding into regions already evacuated by earlier SNe are probably very faint.