The smart control of droplet transport through surface structures and external fields provides exciting opportunities in engineering fields of phase change heat transfer, biomedical chips, and energy harvesting. Here we report the wedge-shaped slippery lubricant-infused porous surface (WS-SLIPS) as an electrothermal platform for active droplet manipulation. WS-SLIPS is fabricated by infusing a wedge-shaped superhydrophobic aluminum plate with phase-changeable paraffin. While the surface wettability of WS-SLIPS can be readily and reversibly switched by the freezing-melting cycle of paraffin, the curvature gradient of the wedge-shaped substrate automatically induces an uneven Laplace pressure inside the droplet, endowing WS-SLIPS the ability to directionally transport droplets without any extra energy input. We demonstrate that WS-SLIPS features spontaneous and controllable droplet transport capability to initiate, brake, lock, and resume the directional motion of various liquid droplets including water, saturated NaCl solution, ethanol solution, and glycerol, under the control of preset DC voltage (∼12 V). In addition, the WS-SLIPS can automatically repair surface scratches or indents when heated and retain the full liquid-manipulating capability afterward. The versatile and robust droplet manipulation platform of WS-SLIPS can be further used in practical scenarios such as laboratory-on-a-chip settings, chemical analysis and microfluidic reactors, paving a new path to develop advanced interface for multifunctional droplet transport.