Background/Objectives: Figurative language is a central tool for enriching spoken and written languages, and it is important for building social relationships. Difficulties in figurative language understanding may impair social adjustment. Some studies have found more gaps in the understanding of irony and idioms among children with autism spectrum disorder (ASD) compared to those of their peers with typical development (TD). To date, no studies have examined the relationship between the ability to understand social situations (as a separate ability) and the ability to understand irony and idioms. The present study examined the roles of theory of mind (ToM) and social situation understanding in the comprehension of idioms and ironic criticism. Methods: The current study included 58 participants aged 8–11, including 28 children with high-functioning ASD and 30 children with TD matched by age, gender, and nonverbal intelligence. All the participants completed a ToM questionnaire that assesses their understanding of others’ intentions, as well as a questionnaire pertaining to their comprehension of social situations, ironic criticism, and idioms. Results: TD children outperformed the autistic children in idiom and irony understanding, as well as in ToM and social situation understanding. Understanding social situations and ToM contributed to idiom and irony understanding, with ToM ability uniquely contributing to irony (but not to idiom) understanding. Path analysis revealed that social cognitive abilities mediated the link between group affiliation and vocabulary, affecting figurative language comprehension. Conclusions: The present study demonstrates that social cognition skills influence the ability to understand ironic criticism and idioms, mediating the association between vocabulary and figurative language comprehension.