The low stability of most superhydrophobic materials is one of the hurdles faced in terms of their practical applications. Inspired by mussel and lotus leaf, we report the fabrication of durable superhydrophobic/superoleophilic polyurethane (PU) sponges for the selective removal of organic pollutants from water. The superhydrophobic/superoleophilic PU sponges are prepared through in-turn covalent modification of PU sponges with polydopamine, silver nanoparticles, and dodecyl mercaptan. The morphology and surface chemical composition of the sponges are characterized by scanning electron microscopy and X-ray photoelectron spectroscopy. In addition, the wetting behaviors, stability, and oil/water separation performance of the superhydrophobic sponges are studied. The modified PU sponges show promising superhydrophobic and superoleophilic properties. The sponge has a water contact angle of about 155° and a shedding angle of approximately 3°, whereas the contact angle of oil is around 0°. In addition, the superhydrophobic coating on the PU sponge exhibits excellent mechanical, chemical, and environmental stability, for example, upon laundering, intensive scalpel scratching, long-duration immersion in organic liquids and oils, and subjection to harsh temperatures and UV irradiation. Moreover, the superhydrophobic sponge can be used repeatedly for the selective and quick absorption of various insoluble organic pollutants (for example, petrol, crude oil, and chloroform) from water with high separation efficiency.