MC is not dead. Aegiana's longsword is made of mithral, which is a vampire's weakness in that world. Thing is, Inori is a different type of vampire, having become one in a different world, and therefore has a different weakness--that being silver. Additionally, since Inori can infinitely regenerate any part of his body provided he has blood (and HP), his weak point is his heart, rather than his head.
The upshot of all this is that it's a bait to get Aegiana to lower her guard, and it works. Knight-lady gets killed, but not before letting Inori know that despite being the "Strongest Human", she's no match for her master, thus setting up the next big opponent to beat. So then Inori knocks out the Hero, tosses him and the other summoned students into a magically-shielded jail cell, grabs the former second princess and torches the castle before leaving.