Building on recent work by Chandar+ (2020, J/ApJ/890/150), we construct X-ray luminosity functions (XLFs) for different classes of X-ray binary (XRB) donors in the nearby star-forming galaxy M83 through a novel methodology. Rather than classifying low-versus high-mass XRBs based on the scaling of the number of X-ray sources with stellar mass and star formation rate, respectively, we utilize multiband Hubble Space Telescope imaging data to classify each Chandra-detected compact X-ray source as a low-mass (i.e., donor mass <~3M_{sun}_), high-mass (donor mass >~8M_{sun}_), or intermediate-mass XRB based on either the location of its candidate counterpart on optical color-magnitude diagrams or the age of its host star cluster. In addition to the standard (single and/or truncated) power-law functional shape, we approximate the resulting XLFs with a Schechter function. We identify a marginally significant (at the 1{sigma}-to-2{sigma} level) exponential downturn for the high-mass XRB XLF, at l~38.48_-0.33_^+0.52^ (in log CGS units). In contrast, the low- and intermediate-mass XRB XLFs, as well as the total XLF of M83, are formally consistent with sampling statistics from a single power law. Our method suggests a non-negligible contribution from low- and possibly intermediate-mass XRBs to the total XRB XLF of M83, i.e., between 20% and 50%, in broad agreement with X-ray-based XLFs. More generally, we caution against considerable contamination from X-ray emitting supernova remnants to the published, X-ray-based XLFs of M83, and possibly all actively star-forming galaxies.