EDIT: Since playtesting and developing this spellcasting option, it has shifted into the domain of the sorcerer. Not only is that class a better match conceptually, but it is also in dire need of more subclasses. Check out the sorcerer version of blood magic here.
WIZARD: BLOOD MAGE
Within your veins lies the darkest and most dangerous form of magic. Blood is a powerful arcane channeler. Only the foolish or the very wise tamper with it as a component, and those who do often suffer as much as they excel. As a blood mage, you substitute self-mutilation for study. You may not be as well read as your counterparts in other arcane traditions, but the path you’ve chosen taxes the body, not the mind.
Some blood mages discover these occult secrets in ancient grimoires, learning to carve hideous but powerful symbols in their flesh. Others enter the apprenticeship of a vile mentor who personally instructs them. Whether you use blood magic to help others or to serve your own ambitions, it is a practice that leaves scars—literal and figurative.
When you select this tradition at 2nd level, you learn the dark arts necessary to turn your own blood into an arcane enhancement. Instead of using the spell slots listed on the Wizard table in the Player’s Handbook, you spend hit points to cast spells. The hit point cost of a spell is determined by its level, as shown on the Hit Point Cost table. Your blood replaces the material components for any spell you cast this way.
When you cast a spell of 1st level or higher, you reduce your current hit points by the number corresponding to the spell’s level. You can’t reduce your current hit points to less than 1 when casting, and you can’t cast a spell of a level higher than you would normally have access to on the Wizard table. You can’t spend temporary hit points to cast spells.
If you wish to cast a spell at a higher level, use the hit point cost of the level at which you’re casting it.
When you choose this tradition at 2nd level, your blood begins to resist the effects of outside magic. You have advantage on Charisma saving throws against magical effects. When you are the recipient of magical healing, you must expend a hit die in order to benefit from it. If you choose not to spend a hit die, the magic has no effect on you.
HIT POINT COST
Spell Level HP Cost
Additionally, the temperature of your blood becomes intolerably high. You are in a constant state of physical agitation and discomfort, and you find yourself going to extreme lengths to sooth it. For example, you might refuse to set foot in a room where a fire is burning in the hearth, or you might flee the sight of hot food or drink. You have odd physical tics that others find eccentric or off-putting because of the eternal fire raging in your veins. Objects and creatures that touch your blood take 1 fire damage. You are immune to damage from touching your own blood.
At 6th level, your connection to the primordial powers is strong enough to protect you from the elements. When you’re below half your hit point maximum, you have resistance to cold, fire, lightning, and poison damage.
Starting at 10th level, you can draw on the soul force of nearby creatures to make your lifeblood course stronger. When you are within 10 feet of a living creature, you can use your action to spend a hit die and gain temporary hit points equal to your wizard level + your Intelligence modifier.
At 14th level, your arcane spells send a swirl of steaming blood around you. If you’re maintaining concentration on a spell when a creature hits you with a melee attack, you can use your reaction to teleport 5 feet. The attacker must succeed on a Dexterity saving throw vs. your spell save DC or miss with the attack.