RNA exosomopathies, a growing family of tissue-specific diseases, are linked to missense mutations in genes encoding the structural subunits of the conserved 10-subunit exoribonuclease complex, the RNA exosome. Such mutations in the cap subunit gene EXOSC2 cause the novel syndrome SHRF (Short stature, Hearing loss, Retinitis pigmentosa and distinctive Facies). In contrast, exosomopathy mutations in the cap subunit gene EXOSC3 cause pontocerebellar hypoplasia type 1b (PCH1b). Though having strikingly different disease pathologies, EXOSC2 and EXOSC3 exosomopathy mutations result in amino acid substitutions in similar, conserved domains of the cap subunits, suggesting that these exosomopathy mutations have distinct consequences for RNA exosome function. We generated the first in vivo model of the SHRF pathogenic amino acid substitutions using budding yeast by introducing the EXOSC2 mutations in the orthologous S. cerevisiae gene RRP4. The resulting rrp4 mutant cells have defects in cell growth and RNA exosome function. We detect significant transcriptomic changes in both coding and non-coding RNAs in the rrp4 variant, rrp4-G226D, which models EXOSC2 p.Gly198Asp. Comparing this rrp4-G226D mutant to the previously studied S. cerevisiae model of EXOSC3 PCH1b mutation, rrp40-W195R, reveals that these mutants have disparate effects on certain RNA targets, providing the first evidence for different mechanistic consequences of these exosomopathy mutations. Congruently, we detect specific negative genetic interactions between RNA exosome cofactor mutants and rrp4-G226D but not rrp40-W195R. These data provide insight into how SHRF mutations could alter the function of the RNA exosome and allow the first direct comparison of exosomopathy mutations that cause distinct pathologies.