A device for grinding a cutting tool uses a rotatable grindstone and a tool holder for mounting the cutting tool. The device guides the tool, mounted in the tool holder, along an intended plane, which is tangential to a peripheral surface of the rotatable grindstone, using a practically linear contact between the rotatable grindstone and the cutting tool. By moving the tool holder, with the mounted cutting tool, along the intended plane, this plane is transferred to an unbevelled side of the cutting tool.