The natural tendency for humans to make and break relationships is thought to facilitate the emergence of cooperation. In particular, allowing conditional cooperators to choose with whom they interact is believed to reinforce the rewards accruing to mutual cooperation while simultaneously excluding defectors. Here we report on a series of human subjects experiments in which groups of 24 participants played an iterated prisoner’s dilemma game where, critically, they were also allowed to propose and delete links to players of their own choosing at some variable rate. Over a wide variety of parameter settings and initial conditions, we found that dynamic partner updating significantly increased the level of cooperation, the average payoff stop layers, and the assortativity between cooperators. Even relatively slow update rates were sufficient to produce large effects, while subsequent increases to the update rate had progressively smaller, but still positive, effects. For standard prisoner’s dilemma payoffs, we also found that assortativity resulted predominantly from cooperators avoiding defectors, not by severing ties with defecting partners, and that cooperation correspondingly suffered. Finally, by modifying the payoffs to satisfy two novel conditions, we found that cooperators did punish defectors by severing ties, leading to higher levels of cooperation that persisted for longer.