I managed to kill it in the full version, on a run where I had the Crimson Shroud and probably other health/armor buffs.
So Death is technically killable in the demo, but from a practical sense it's impossible.
He has absurdly high health, multiplied by your level when he spawns, and does absurdly high damage (I think he just oneshots you regardless of HP), and knockback has the opposite effect on him. If you were somehow able to keep him frozen indefinitely, it would take you forever to kill him.