"he shall be put to death": in beth-din. You say this, but perhaps it need not be in beth-din. It is, therefore, written (Numbers 35:12) "and the slayer shall not die until he stand before the congregation for judgment." What, then, is the intent of "he shall be put to death"? In beth-din.
He Shall Be Put to Death in Beth-din
Mekhilta Tractate Nezikin 4:6