Suicide and homicide are considered important problems in public health. This study aims to identify the cognitive performance of suicidal and homicidal behaviors in people with schizophrenia spectrum disorders, as well as examining whether there are shared neuropsychological mechanisms. A systematic review of the recent literature was carried out from September 2012 to June 2022 using the Medline (via PubMed), Scopus, Embase, and Cochrane databases. Among the 870 studies initially identified, 23 were finally selected (15 related to suicidal behaviors and 8 to homicidal behaviors). The results evidenced a relationship between impairment of cognitive performance and homicidal behavior; meanwhile, for suicidal behaviors, no consistent results were found. High neuropsychological performance seems to act as a protective factor against violent behavior in people with schizophrenia spectrum disorders, but not against suicidal behavior; indeed, it can even act as a risk factor for suicidal behavior. To date, there is insufficient evidence that shared neurocognitive mechanisms exist. However, processing speed and visual memory seem to be affected in the presence of both behaviors.