Many young people with autism spectrum disorder display 'challenging behaviours', characterised by externalising behaviour and self-injurious behaviours. These behaviours can have a negative impact on a young person's well-being, family environment and educational achievement. However, the development of effective interventions requires greater knowledge of autism spectrum disorder-specific models of challenging behaviours. Autism spectrum disorder populations are found to demonstrate impairments in different cognitive domains, namely social domains, such as theory of mind and emotion recognition, but also non-social domains such as executive functioning and sensory or perceptual processing. Parent-rated self-injurious behaviour and externalising behaviours, and neurocognitive performance were assessed in a population-derived sample of 100 adolescents with autism spectrum disorder. Structural equation modelling was used to estimate associations between cognitive domains (theory of mind, emotion recognition, executive functioning and perceptual processing) and self-injurious behaviour and externalising behaviours. Poorer theory of mind was associated with increased self-injurious behaviour, whereas poorer perceptual processing was associated with increased externalising behaviours. These associations remained when controlling for language ability. This is the first analysis to examine how a wide range of neurocognitive domains relate to challenging behaviours and suggests specific domains that may be important targets in the development of interventions in adolescents with autism spectrum disorder.