Floating vessel-type oil collecting devices based on sorbent materials present potential solutions to oil spill cleanup that require a massive amount of sorbent material and manual labor. Additionally, continuous oil extraction from these devices presents opportunities for highly energy-efficient oil skimmers that use gravity as the oil/water separation mechanism. Herein, a sorbent-based oil skimmer (SOS) is developed with a novel funnel-shaped sorbent and vessel design for efficient and continuous extraction of various oils from the water surface. A carbon black (CB) embedded polydimethylsiloxane (PDMS) sponge material is characterized and used as the sorbent in the SOS. The nanocomposite sponge formulation is optimized for high reusability, hydrophobicity, and rapid oil absorption. Joule heating functionality of the sponge is also explored to rapidly absorb highly viscous oils that are a significant challenge for oil spill cleanup. The optimized sponge material with the highest porosity and 15 wt% CB loading is tested in the SOS for large-scale oil spill extraction tests and shows effective cleaning of oil spilled on the water surface. The SOS demonstrates a high maximum extraction rate of 200 mL/min for gasoline and maintains a high extraction rate performance upon reuse when the sponge funnel is cleaned and dried.