The evolved capacity for third-party punishment is considered crucial to the emergence and maintenance of elaborate human social organization and is central to the modern provision of fairness and justice within society. Although it is well established that the mental state of the offender and the severity of the harm he caused are the two primary predictors of punishment decisions, the precise cognitive and brain mechanisms by which these distinct components are evaluated and integrated into a punishment decision are poorly understood. Using fMRI, here we implement a novel experimental design to functionally dissociate the mechanisms underlying evaluation, integration, and decision that were conflated in previous studies of third-party punishment. Behaviorally, the punishment decision is primarily defined by a superadditive interaction between harm and mental state, with subjects weighing the interaction factor more than the single factors of harm and mental state. On a neural level, evaluation of harms engaged brain areas associated with affective and somatosensory processing, whereas mental state evaluation primarily recruited circuitry involved in mentalization. Harm and mental state evaluations are integrated in medial prefrontal and posterior cingulate structures, with the amygdala acting as a pivotal hub of the interaction between harm and mental state. This integrated information is used by the right dorsolateral prefrontal cortex at the time of the decision to assign an appropriate punishment through a distributed coding system. Together, these findings provide a blueprint of the brain mechanisms by which neutral third parties render punishment decisions. Punishment undergirds large-scale cooperation and helps dispense criminal justice. Yet it is currently unknown precisely how people assess the mental states of offenders, evaluate the harms they caused, and integrate those two components into a single punishment decision. Using a new design, we isolated these three processes, identifying the distinct brain systems and activities that enable each. Additional findings suggest that the amygdala plays a crucial role in mediating the interaction of mental state and harm information, whereas the dorsolateral prefrontal cortex plays a crucial, final-stage role, both in integrating mental state and harm information and in selecting a suitable punishment amount. These findings deepen our understanding of how punishment decisions are made, which may someday help to improve them.