The high-efficient, eco-friendly and low-energy cleanup of viscous crude oil spills is still a global challenge. Emerging absorbents with self-heating function are promising candidates due to that they can significantly decrease crude oil viscosity via in-situ heat transfer so as to accelerate remediation. Herein we developed a novel multifunctional magnetic sponge (P-MXene/FeO@MS) with outstanding solar/electro-thermal performance by facilely coating TiCT MXene, nano-FeO and polydimethylsiloxane onto melamine sponge for fast crude oil recovery. Superior hydrophobicity (water contact angle of 147°) and magnetic responsivity allowed P-MXene/FeO@MS to be magnetically driven for oil/water separation and easy recycling. Owing to excellent full-solar-spectrum absorption (average absorptivity of 96.5 %), effective photothermal conversion and high conductivity (resistance of 300 Ω), P-MXene/FeO@MS possessed remarkable solar/Joule heating capability. The maximum surface temperature of P-MXene/FeO@MS could quickly reach 84 °C under a solar irradiation of 1.0 kW/m and 100 °C after applying a voltage of 20 V. The generated heat induced a significant decrease of crude oil viscosity, enabling the composite sponge to absorb more than 27 times its weight of crude oil within 2 min (1.0 kW/m irradiation). More importantly, by means of the synergistic effect of Joule heating and solar heating, a pump-assisted absorption device based on P-MXene/FeO@MS was able to realize the high-efficiency and all-day continuous separation of high-viscosity oil on water surface (crude oil flux = 710 kg m h). The new-typed multifunctional sponge provides a competitive approach for dealing with large-area crude oil pollution.