Image-adaptive lookup tables (LUTs) have achieved great success in real-time image enhancement tasks due to their high efficiency for modeling color transforms. However, they embed the complete transform, including the color component-independent and the component-correlated parts, into only a single type of LUTs, either 1D or 3D, in a coupled manner. This scheme raises a dilemma of improving model expressiveness or efficiency due to two factors. On the one hand, the 1D LUTs provide high computational efficiency but lack the critical capability of color components interaction. On the other, the 3D LUTs present enhanced component-correlated transform capability but suffer from heavy memory footprint, high training difficulty, and limited cell utilization. Inspired by the conventional divide-and-conquer practice in the image signal processor, we present SepLUT (separable image-adaptive lookup table) to tackle the above limitations. Specifically, we separate a single color transform into a cascade of componentindependent and component-correlated sub-transforms instantiated as 1D and 3D LUTs, respectively. In this way, the capabilities of two subtransforms can facilitate each other, where the 3D LUT complements the ability to mix up color components, and the 1D LUT redistributes the input colors to increase the cell utilization of the 3D LUT and thus enable the use of a more lightweight 3D LUT. Experiments demonstrate that the proposed method presents enhanced performance on photo retouching benchmark datasets than the current state-of-the-art and achieves real-time processing on both GPUs and CPUs.