Magically, blood is a powerful connection. Blood is your signature, blood is you. We could go further down fantasy magic paths and posit that this character's blood has the ability to change other people into them, causing massive problems as a significant portion of their body becomes someone else who must be attacked by the immune system. And possibly with the converted portion's immune system attacking the unmodified parts as well.
If they are attacking with their blood by using some kind of telekenisis then you could do some nasty stuff. Spray it in someone's nose. You know how when you get a sinus infection it feels like your head's gonna explode? Multiply that by a bit. Get it down someone's throat, use a thick blob to jerk the esophagus around, push down into the intestines and tie those into a hideous painful knot. Or push up into them from the other end if this is an X-rated affair.
Get it into someone's veins and you can do even worse. Make a nice big clot right in the middle of a major artery, jam up one of the heart's valves, or how about a lot of pressure on a blood vessel in the brain? That's pretty fatal.