A controversial proposal to build the mammoth ‘Site C’ dam on the Peace River in northwestern Canada offers an opportunity to explore the intersections of climate and migration issues under debate in international environmental governance circles. Site C threatens to flood traditional fishing spots and traplines of Indigenous peoples in the name of the ‘green energy’ economy. We consider how people displaced by renewable energy projects justified as climate mitigation policies might constitute a different kind of ‘climate refugee’ in that they are ‘displaced without moving’ – the connections between the land and the people are severed to the extent that what is lost is the ability of the people to sustain themselves in a place. We demonstrate that the focus on ‘security’ and ‘risk’ in dominant approaches to the phenomenon of climate migration within the international regimes of human rights and climate governance produces contemporary commitments to ‘migration management’ and a prescription for ‘planned relocations’ that employ an abstract conception of the ‘climate migrant’. The analysis reveals that the dominant international legal order on climate migration is devoid of meaningful consideration of ongoing, embodied practices of living on the land. Its abstract, universalist conceptions of land, labour and livelihoods deny the possibility of people's meaningful relations with specific places and obscure the actual ‘loss and damage’ that transpires when real, material and ecological relations that ground people's connections with land are severed. We conclude that, without concerted resistance and a focus on re-making the underlying structural relations, a policy emphasis on renewable energy development as ‘climate mitigation’ is likely to continue to produce the same inequitable patterns of benefits and burdens as climate change itself.