In this work, organic solvent-induced shape memory poly(ethylene-co-vinyl acetate) (EVA) monoliths are developed based on a facile thermally induced phase separation (TIPS) method. The obtained EVA monoliths show three-dimensional (3D) interconnected porous structures with tunable porosities from 54.52 % to 73.01 %, average pore sizes from 4.8 to 17.5 mu m, and satisfactory shape memory properties. Utilizing the hydrophobic nature of EVA, the porous monoliths effectively separate oil/water by selective oil absorption. Moreover, the EVA monoliths exhibiting oil-triggered shape recovery are designed to be expandable oil absorbers, which shows doubled volumetric absorption capacities of 1.96-2.48 g/cm3 for pentane, hexane, and octane with a prefixed compression strain of 70 %. The uniform porous structures of monolithic materials and shape memory properties of semi-crystalline elastomers are well combined in this work, which will provide new possibilities for the design of smart porous materials or structures for novel oil absorbers, thermal insulators, and flow reactors.