Spontaneous removal of condensed matter from surfaces is exploited in nature and in a broad range of technologies to achieve self-cleaning(1,2), anti-icing(3-6) and condensation control(7,8). But despite much progress(5-7,9-14), our understanding of the phenomena leading to such behaviour remains incomplete, which makes it challenging to rationally design surfaces that benefit from its manifestation(15-18). Here we show that water droplets resting on superhydrophobic textured surfaces in a low-pressure environment can self-remove through sudden spontaneous levitation and subsequent trampoline-like bouncing behaviour, in which sequential collisions with the surface accelerate the droplets. These collisions have restitution coefficients (ratios of relative speeds after and before collision) greater than unity(19) despite complete rigidity of the surface, and thus seemingly violate the second law of thermodynamics. However, these restitution coefficients result from an overpressure beneath the droplet produced by fast droplet vaporization while substrate adhesion and surface texture restrict vapour flow. We also show that the high vaporization rates experienced by the droplets and the associated cooling can result in freezing from a supercooled state(20,21) that triggers a sudden increase in vaporization, which in turn boosts the levitation process. This effect can spontaneously remove surface icing by lifting away icy drops the moment they freeze. Although these observations are relevant only to systems in a low-pressure environment, they show how surface texturing can produce droplet-surface interactions that prohibit liquid and freezing water-droplet retention on surfaces.