In this study, we compared three domains of social cognition (emotion processing, mentalization, and attribution bias) to clinical and computational language measures in 63 participants with schizophrenia spectrum disorders. Based on the active inference model for discourse, we hypothesized that emotion processing and mentalization, but not attribution bias, would be related to language disturbances. Clinical ratings for speech disturbance assessed disorganized and underproductive dimensions. Computational features included speech graph metrics, use of modal verbs, use of first-person pronouns, cosine similarity of adjacent utterances, and measures of sentiment; these were represented by four principal components characterizing content-rich speech, insular speech, local coherence, and affirmative speech. We found that higher clinical ratings for disorganized speech predicted greater impairments in both emotion processing and mentalization, and that these relationships remained significant when accounting for demographic variables, overall psychosis symptoms, and verbal ability. Similarly, computational features reflecting insular speech also consistently predicted greater impairment in emotion processing. There were notable trends for underproductive speech and decreased content-rich speech predicting mentalization ability. Exploratory longitudinal analyses in a small subset of participants (n=17) found that improvements in both emotion processing and mentalization were predicted by improvements in disorganized speech. Attribution bias did not demonstrate strong relationships with language measures. Altogether, our findings are consistent with the active inference model of discourse and suggest greater emphasis on treatments that target social cognitive and language systems.