A non-rotary cutting tool which is to be moved relative to a workpiece in a predetermined direction for cutting the workpiece, with its rake face being held substantially perpendicular to the predetermined direction. The cutting tool includes (a) a generally cylindrical shank portion, and (b) a generally semi-cylindrical body portion which has an outer circumferential surface constituted by the rake face and a semi-cylindrical surface. The semi-cylindrical body portion has a cutting edge which is defined by an edge of the rake face and which is covered with a diamond coating. Also disclosed is a process of machining a scroll member of a scroll compressor by using this non-rotary cutting tool.