In the mid-20th century, scientists began to collect and freeze blood samples for a range of purposes. This article considers the broader implications of scientific freezing for conceptions of time and life by drawing on empirical research with scientists associated with a large collection of samples assembled from Indigenous Australians in the 1960s. We first review some key critiques of cryopreservation posed by Indigenous scholars and by science and technology studies. We then propose ‘cryopolitics’ as a concept to express the various political, ethical and temporal conundrums presented by the practice of freezing. We frame cryopolitics as a mode of Michel Foucault’s biopolitics. If biopolitical assemblages make live and let die, cryopolitical ones reveal the dramatic consequences of mundane efforts to make live and not let die. In our case study, we argue that frozen blood vacillates between two cryopolitical states, ‘latent life’ and ‘incomplete death’. Samples seen as latent life cannot be destroyed; samples understood as incomplete death require destruction. A state of incomplete death can be resolved through the return of blood samples to the Indigenous groups they were collected from, a process that has occurred in North America. Our cryopolitical analysis suggests another potential resolution: reviving a form of latent life aligned with futures envisaged by Indigenous communities themselves.