We report the results from a spectrophotometric study sampling the roughly 300 candidate supernova remnants (SNRs) in M83 identified through optical imaging with Magellan/IMACS and HST/WFC3. Of the 118 candidates identified based on a high [S II] $lambdalambda$ 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 [O III] 5007 $lambda$ 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 (over 1000 km/s) emission lines characteristic of ejecta-dominated SNRs, beyond the known SN1957D remnant. The other 20 [O III]-selected candidates include planetary nebulae, compact H II regions, and one background QSO. Although our spectroscopic sample includes 22 SNRs smaller than 11 pc, none of the other objects shows broad emission lines; instead their spectra stem from relatively slow (< 200 km/s) radiative shocks propagating into the metal-rich interstellar medium of M83. With six SNe in the past century, one might expect more of M83s 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.