Punishments were Inflicted by the People
Source: TTT
Numbers 15:35, 36
And the LORD said to Moses, “The man must surely be put to death. The whole congregation is to stone him outside the camp.” / So the whole congregation took the man outside the camp and stoned him to death, as the LORD had commanded Moses.
Deuteronomy 13:9
Instead, you must surely kill him. Your hand must be the first against him to put him to death, and then the hands of all the people.