When I lose all my hearts in combat and I have a fairy in my inventory, it expends a fairy to heal me to full health. Sometimes, I don't want it to do that and I'd rather die and respawn. Is there a way to stop the fairy from healing me?
Beyond releasing the fairies ahead of time, this is not possible. You can however disable the renewable ability acquired after completing a Devine Beast, which behaves like a super fairy, as noted by Seiyria:
You can disable the ability, actually... just go to Special Items, choose it, and turn it off.
Your only option to avoid using fairies is to manually load your last save, which is what a Game Over would offer.