3D porous materials are of great interest in many areas of study, but it is still difficult to prepare those with high elasticity and low thermal conductivity via facile methods. Here, superelastic laponite/silicone (LS) composite sponges with low thermal conductivity are prepared via a simple approach. The LS sponges were analyzed by various characterization methods. The content of laponite nanosheets in LS sponges has a great influence on the microstructure, comprehensive mechanical properties, and thermal conductivity. LS sponges feature (i) high mechanical strength, compressibility, and elasticity, (ii) excellent superhydrophobicity/superoleophilicity, and (iii) low thermal conductivity. Consequently, LS sponges could be used for water purification, for example, oil/water separation and solar-driven interfacial evaporation in combination with carbon nanotubes (CNTs). The LS/CNTs solar evaporator has a remarkable evaporation rate of 1.77 kg m −2 h −1 for the 3.5 wt % NaCl aqueous solution under 1 kW m −2 irradiation and high salt resistance. We foresee that this study will promote the development of new 3D porous materials and their applications.