Indexable cutting unit heads for parting and grooving are used as part of modular tool system to remove sections of material or add grooves to workpieces. They perform like solid parting and grooving tools, but mount to a compatible quick-change toolholder. These cutting heads can be replaced without removing the toolholder from the machine. The heads hold multi-edged inserts that can be rotated (indexed) to expose a fresh cutting edge when the old one dulls. The inserts can be exchanged for new ones of the same style or a different style that's compatible with the cutting head. Indexable parting and grooving tools require fewer tool changes than solid tools in high-volume metalworking and fabrication applications with high speeds, high feeds, and difficult-to-machine materials.