Oil-in-water (O/W) emulsions and gel emulsions which are stabilized by surfactants for more than 5 months have been successfully separated by a simple gravity-driven agitation-assisted device. The device contains a rotating magnetic stir bar and a flexible superhydrophobic/superoleophilic Cu mesh which has been folded into the desired three-dimensional shape. The emulsions were prepared by mixing various fractions of alkane and water (99-1%) stabilized by a water-soluble surfactant. For low water fractions which contained higher concentrations of the surfactant, solid-like gel emulsions were obtained. The stress-driven process was found to effectively separate stable emulsions with a separation efficiency ≥ 98% and gel emulsions with a separation efficiency as high as 96%. The mechanism for oil recovery from stable emulsions by our stress-driven device is based on the momentary breakage of the water barrier layer (superhydrophobicity) and the enhancement of the oil-mesh contact leading to oil permeation (superoleophilicity). For gel emulsions, the additional function of the stress is to induce a temporary transformation from the solid-like gel into a liquid-like state. Our methodology can be employed for an efficient separation of highly stable O/W emulsions and gel emulsions that are often produced by industrial processes.