The Boycotts, Divestment and Sanctions (BDS) Movement is a global political campaign led by Palestinian civil society since 2005. Its official aim is to put pressure on Israel to radically change its policies towards Palestinians. Drawing on Gilles Deleuze and Félix Guattari’s political philosophy, this paper discusses the BDS movement by looking into its affective powers. In particular, it claims that, above all else, acting as a political mediator BDS weakens the predominance of the current assemblage of public discourses on Israel-Palestine.