A rotatable cutting tool unit of a tool assembly for a cutting machine that is used in conjunction with an associated method of cutting provides several novel aspects. The tool arrangement, which includes two tool units, includes first and second disk-shaped tools rotatable about an axis. The tools define maximum tool arrangement boundaries along the axis. A driving arrangement, at an axial location between the first and second tools, supports the first and second tools for rotation and transfers driving force. A radially outer periphery of the driving arrangement is at a radius less than a radius of a peripheral cutting edge portion of the first tool and less than a radius of a peripheral cutting edge portion of the second tool.