Adolescence is a key period for neurocognitive maturation where deviation from normal developmental trajectories may be tied to adverse mental health outcomes. Cognitive disruptions have been noted in populations at risk for psychosis and are known to accompany periods of sleep deprivation. This study aims to assess the role of cognition as a mediator between sleep disruptions and psychosis risk. A cohort of 3801 high school students (51% female, mean age = 12.8, SD = 0.45 years) was recruited from 31 Montreal high schools. Measures of sleep, psychotic-like experiences, inhibition, working memory, perceptual reasoning, and delayed recall were collected from participants on a yearly basis over the five years of their high school education. A multi-level model mediation analysis was performed controlling for sex and time squared. Response inhibition was shown to be associated with, and to mediate (B = −0.005, SD = 0.003, p = 0.005*) the relationship between sleep disruptions (B = −0.011, SD = 0.004, p < 0.001*) and psychotic-like experiences (B = 0.411, SD = 0.170, p = 0.005*). Spatial working memory deficits on a given year were associated with a higher frequency of psychotic-like experiences that same year (B = −0.046, SD = 0.018, p = 0.005*) and the following year (B = −0.051, SD = 0.023, p = 0.010*), but were not associated with sleep disturbances. No significant associations were found between our variables of interest and either delayed recall or perceptual reasoning at the within person level. Findings from this large longitudinal study provide evidence that the association between sleep disruptions and psychosis risk is specifically mediated by inhibitory rather than general cognitive impairments. The association of spatial working memory, response inhibition, and sleep disruptions with psychotic-like experiences suggests that these factors may represent potential targets for preventative interventions.