Patients with schizophrenia are often described as impaired in several cognitive domains. Specifically, patients with schizophrenia often exhibit problems in solving tasks requiring theory of mind (ToM), i.e., the ability to ascribe mental states to oneself and others, communicative-pragmatic ability, i.e., the ability to use language and non-verbal expressive means to convey meaning in a given context, and executive functions (EF). This study aims to investigate the role of cognitive functions, such as general intelligence, selective attention, processing speed, and especially EF (working memory, cognitive flexibility, inhibition, and planning), and ToM in explaining the performance of individual with schizophrenia in comprehending and producing communicative acts expressed with different communicative intentions (i.e., sincere, deceitful, and ironic), and realized through linguistic and extralinguistic/non-verbal expressive means. Thirty-two patients with schizophrenia and an equal number of healthy controls performed tasks aiming to investigate their capacity to comprehend and produce sincere, deceitful, and ironic communicative acts in addition to a series of cognitive tasks evaluating EF and ToM. The results indicated that individuals with schizophrenia performed worse than the controls in the comprehension and production of all pragmatic phenomena investigated, as well as in all the cognitive functions examined. The patients with schizophrenia also exhibited an increasing trend of difficulty in comprehending and producing sincere, deceitful, and ironic communicative acts expressed through either linguistic or extralinguistic means. Furthermore, a multiple regression analysis of the patients’ performance on the pragmatic tasks revealed that overall, the role of attention, general intelligence, and processing speed did not appear to significantly explain the patients’ communicative-pragmatic performance. The inclusion of EF into the analysis did not contribute to increase the explained variance of the patients’ ability to comprehend and produce the various pragmatic phenomena investigated. Only the addition of ToM could significantly increase the explained variance, but only in the comprehension and production of deceit expressed by language and the production of sincere communicative acts, also limited to linguistic production. We conclude that neither EF nor ToM are able to explain the decreasing trend detected in the patients’ pragmatic performance.