What's the purpose of this part of Topeak Hexus II multitool?
This is the other clip end of the tire lever.  The tire lever with the clip is intended to go in first and hold the lever in place (by clipping onto a spoke) while you use the other lever (with your hand) to go around the rim and break the bead.

If you check the "Using Tire Levers" section of the manual, you can see the clip being used to secure the first lever to a spoke.