It would probably be beneficial to ask the crystal if you have animistic beliefs. Personally, I've never found lore or any mention of breaking crystals to be a bad thing as they have been cut and shaped since humans could craft with them.
As you are working with the energy of the crystal and that is what takes effect, you probably wouldn't need three physical crystals so long as you call up the energy of the other two (or evoke the energy of the crystal in three spots) for the spell you are trying for. Remember that you can imbue the energy into other materials.
If you are still looking to have three pieces of black tourmaline, I would look into what it takes to cut crystals and try it out with a different crystal you are not as uneasy to mess up while you're learning. Then as you are comfortable, you can cut three pieces out of the chunk you'd have.