Quartz crystal is crystallized silicon dioxide (SiO2). Quartz crystals are quite hard, around 7 on the Mohs scale, just under diamond which, along with concerns such as silicate dust makes these crystals challenging to cut. Most quartz crystals are small in size with pyramidal ends. Often one end is broken off from a cluster leaving ragged edges and in order to use the crystals in jewelry those edges need to be cut. This can be done with good protection and the right tools
Wear protective clothing and safety equipment and ventilate your work space. Insert the quartz crystal into your vise so that the area you wish to cut is accessible on the end closest to you (if possible) and with the leather between the metal of the vise and the stone. The stone should be firmly held, but not so tightly as to crush it. Insert the quartz
Squirt mineral oil on your crystal.
Holding your Dremel tool firmly, allow the diamond blade to contact the crystal. Don't push the blade. Allow the blade to work for you. Lift the blade often to keep it from overheating. Add oil as needed.
Rotate the crystal in the vise if it is larger than the depth of your blade or even if your tool gets too low on the stone.
Change your blade to a diamond grinder to clean edges once the cut is completed. Going from a low-grit diamond wheel to progressively higher grits will smooth and polish your crystal.
Vacuum all silicate dust and don't remove your respirator until you go outside of your shop. Silicate dust is quite dangerous to inhale. Wash your crystal with soap and water before handling it.
Don't shake out your clothing. Remove and bag your clothing and launder it at a laundromat (not at home). Wash your boots, gloves and glasses off with water, outside. Dremel doesn't appear to make the larger cutting blades anymore but this vendor on Amazon carries a workable alternative. Using the Dremel flex line with this project will give you better control. You can clean your diamond blade by lightly running it into a brick or piece of concrete block.
Silicate dust will continue to settle and the area where the stone is being cut should be vacuumed and wiped down with water and a rag frequently in order to remove dust that can be inhaled later.