Indexable parting and grooving toolholders have a shank that mounts to a lathe or CNC turning machine and a cutting head that holds an indexable insert or cut-off blade. They are held stationary as the machine rotates the workpiece against the insert to remove sections of material or add grooves to workpieces. The inserts have multiple cutting edges and can be rotated (indexed) to expose a fresh cutting edge when the old one dulls. They can be exchanged for new ones of the same style or a different style that's compatible with the toolholder without removing the toolholder from the machine. These toolholders have through-coolant holes that allow internal coolant flow to reduce friction and heat buildup in high-speed and high-feed applications. 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.