A cutting part (1) for a tool head (2) for a lathe (3) for machining a workpiece (4), having a cutting edge (5) for removing material from the workpiece (4) and having a rake face (6) for guiding away the removed material or cuttings. The problem of providing a cutting part (1) which can be realized in a simple manner and with which lead-free materials can also be machined is solved in that a flat structure (7) is formed in the rake face (6) of the cutting part (1) adjoining the cutting edge (5) for breaking the cuttings. A lathe (3) for machining a workpiece (4), having a tool head (2) is provided with at least one such cutting part (1).