It's right there in the bible... god does not mince words...
If a man has sexual intercourse with a male as one has sexual intercourse with a woman, the two of them have committed an abomination. They must be put to death; their blood guilt is on themselves.
The book of Leviticus (24:27) also states: "Whoever takes a human life shall surely be put to death"
And this appears later in the book than your quote, which implies that if a male having sex with a male should be put to death
it should not be done at the hands of another human.God doesn't ask anyone to kill on behalf of his will. God doesn't save those who sin, that's the punishment.
Additional quotes from the Bible about death include:
Matthew 5:21 "You have heard that it was said to those of old, 'You shall not murder; and whoever murders will be liable to judgement.'"
Deuteronomy 5:17 "You shall not murder."
Exodus 21:12 "Whoever strikes a man so that he dies shall be put to death."
The problem here is, who is "they"? Could they be the Government, which is ok but not us lot?