The evolutionary trend toward increasing complexity and social function is ultimately the result of natural selection's paradoxical tendency to foster cooperation through competition. Cooperating populations ranging from complex societies to somatic tissue are constantly under attack, however, by non-cooperating mutants or transformants, called ‘cheaters’. Structure in these populations promotes the formation of cooperating clusters whose competitive superiority can alone be sufficient to thwart outgrowths of cheaters and thereby maintain cooperation. But we find that when cheaters appear too frequently – exceeding a threshold mutation or transformation rate – their scattered outgrowths infiltrate and break up cooperating clusters, resulting in a cascading loss of social cohesiveness, a switch to net positive selection for cheaters and ultimately in the loss of cooperation. Our findings imply that a critically low mutation rate had to be achieved (perhaps through the advent of proofreading and repair mechanisms) before complex cooperative functions, such as those required for multicellularity and social behaviour, could have evolved and persisted. When mutation rate in our model is also allowed to evolve, the threshold is crossed spontaneously after thousands of generations, at which point cheaters rapidly invade. Probing extrapolations of these findings suggest: (1) in somatic tissue, it is neither social retro-evolution alone nor mutation rate evolution alone but the interplay between these two that ultimately leads to oncogenic transitions; the rate of this coevolution might thereby provide an indicator of lifespan of species, terrestrial or not; (2) the likelihood that extraterrestrial life can be expected to be multicellular and social should be affected by ultraviolet and other mutagenic factors.