Cleaving is the splitting of a diamond rough parallel to one of its triangular, octahedral planes (three grains). Wood has a single grain that can be split with an axe or wedge without too much effort. A diamond can also be split, but since the cleaver is dealing with four possible directions (parallel to each triangular octahedral face), the planning can be a bit more challenging. Some of the more notable diamonds in history were sometimes studied for months before the first strike. This involved more than just figuring out where the cleavage plane lay, but also entailed an intense design for maximum value and weight retention. Once the cleaver decides where the first split is to occur, he notches a kerf in the diamond, which is bruted (scratched) using another sharp diamond held parallel to the cleavage plane. The kerf must be deep enough and in the proper direction. Once the cleaver is satisfied with his kerf, he places a steel wedge in the kerf groove, again holding it parallel to the cleavage plane, and strikes it firmly with a light mallet, splitting the diamond. Many times, especially with large rough, the cleaver may choose to split the diamond into several pieces.

The disadvantage of cleaving is the lack of flexibility in the directions that the stone can be split. There is also a risk of breaking the stone irregularly, incurring a great loss in value. Cleaving is an art in itself, in the overall gamut of diamond cutting.