Social norms are an important element in explaining how humans achieve very high levels of cooperative activity. It is widely observed that, when norms can be enforced by peer punishment, groups are able to resolve social dilemmas in prosocial, cooperative ways. Here we show that punishment can also encourage participation in destructive behaviours that are harmful to group welfare, and that this phenomenon is mediated by a social norm. In a variation of a public goods game, in which the return to investment is negative for both group and individual, we find that the opportunity to punish led to higher levels of contribution, thereby harming collective payoffs. A second experiment confirmed that, independently of whether punishment is available, a majority of subjects regard the efficient behaviour of non-contribution as socially inappropriate. The results show that simply providing a punishment opportunity does not guarantee that punishment will be used for socially beneficial ends, because the social norms that influence punishment behaviour may themselves be destructive.