This paper is a response to the urgent call for redesign of human-nature relations by addressing the need to move away from Modernist dualisms of nature-culture rooted in current unsustainable societies. Thereby, we adopt a procedural conceptualisation of sustainability, based in constructivist social theories, to open up the discussion from two points of departure: biomimicry and urban greening. We explore biomimicry as a possible novel relational approach to human-nature perspectives and interactions, which we seek to translate into urban greening strategies. We argue that urban greening must move towards process-oriented strategies that open up spaces for reflection on and new articulations of human perspectives and relations with nature, thus we take our vantage point in the interpretive flexibility of the biomimicry concept to inspire new possibilities in a local context. Based on initial methodological and conceptual considerations of biomimicry, we take the role of navigators and, through a compositionist design approach, we further develop our translation of biomimicry with sensitivity toward our urban greening context in Østerbro, a neighborhood in Copenhagen, Denmark. We then develop and stage a design experiment in order to make tangible our experimentation with biomimicry as a function for process-oriented urban greening strategies. Through the development and staging of our design experiment, we demonstrate how relations can be mobilised, both socially and materially, around the concept of biomimicry such that growing urban agendas can gain the transformational momentum needed to move toward more sustainable urban futures.