Classical Athens seems to have had an aversion to bloody spectacle. Something the Romans enjoyed. Most punishments for crimes involves paying fines, or exile.
Higherstatus citizens like Socrates who were condemned to death were allowed to drink hemlock poison.
For others, they would tie you to a wooden board and leave you exposed until you died. Again, no blood.
The western obsession with "beheading" as like, the bad kind of murder, as opposed to being blown up, drowned or shot with a gun, needs to be studied in a lab.