What if a bead would be perfect for a project but would work better as half a bead. Grinding it down is the best option because cutting beads requires specialized equipment.
This is a "live and learn" project. Some beads can be split, but most beads do not split well. Check the Mohs scale of hardness for the bead being considered. The lower the number, the higher the success rate will be. Do not consider a bead with a Mohs scale number above 5. The magnesite beads used here have a 3-1/2 to 4 Mohs rating. Consider the cost of the lost beads because not all, if any, of the chosen beads will split well.
Using a sewing awl, turquoise handle, did not go well as the bead debris shows. The awl was too thick. Try a much thinner awl. A thinner awl than the one used here may work better.
Place the tip of the awl in the hole on one side of the bead. Hold the awl upright and use a hammer to lightly tap the point the awl into hole of an 8mm green mosaic magnesite bead. As luck would have it, three different sets of mostly matching cabochons and only had two disasters were the result. The backs were not sanded flat.
Hmm, maybe this would work with larger beads. The same process was tried with 16mm mosaic magnesite beads. After disasters with three beads, it was time to call it quits.
The small green cabochons were used in the above earrings and set in the same manner as the teardrop cabochons.