Background Impairments in executive function characterize offenders with antisocial personality disorder (ASPD) and offenders with psychopathy. However, the extent to which those impairments are associated with ASPD, psychopathy, or both is unknown. Methods The present study examined 17 violent offenders with ASPD and psychopathy (ASPD+P), 28 violent offenders with ASPD without psychopathy (ASPD−P), and 21 healthy non-offenders on tasks assessing cool (verbal working memory and alteration of motor responses to spatial locations) and hot (reversal learning, decision-making under risk, and stimulus-reinforcement-based decision-making) executive function. Results In comparison to healthy non-offenders, violent offenders with ASPD+P and those with ASPD−P showed similar impairments in verbal working memory and adaptive decision-making. They failed to learn from punishment cues, to change their behaviour in the face of changing contingencies, and made poorer quality decisions despite longer periods of deliberation. Intriguingly, the two groups of offenders did not differ significantly from the non-offenders in terms of their alteration of motor responses to spatial locations and their levels of risk-taking, indicated by betting, and impulsivity, measured as delay aversion. The performance of the two groups of offenders on the measures of cool and hot executive function did not differ, indicating shared deficits. Conclusions These documented impairments may help to explain the persistence of antisocial behaviours despite the known risks of the negative consequences of such behaviours.