As others have mentioned, you can’t kill him. He takes damage, but is prevented from death.
If you want the sword, you can have it. In the dream sequence, if you run around where your mother and father are supposed to be saved, and store the sword in the chest in your parents house, it will be there the next time you return to Skalitz. This does not have an effect on the game story, however, and you can’t give it to Radzig.