The idea of execution by decapitation is bizarre and horrific, though for millennia public beheadings around the world were fairly common. It's only in modern times that cutting a person's head off has come to be considered barbaric.
In centuries past, beheading was actually preferable to other common forms of execution (such as being burned alive or disemboweled). In early England beheading was considered a noble, and even honorable, death. Nigel Cawthorne, author of "Public Executions" (2006, Capella Press) notes that "Hanging was usually reserved for the lower classes.
Rebellious noblemen who had been sentenced to be hanged, drawn and quartered for treason were understandably relieved when their sentence was changed to beheading ... knowing that they could make a parting speech before departing this life in a relatively swift and painless manner."
Beheading remains an officially sanctioned method of execution in several Middle Eastern countries.
Though historically decapitation was essentially a means to an end, the beheading element itself carried a powerful message and continues to do so today. There are far cleaner and less gruesome ways to kill a person, but few things make a greater impression on the public than seeing a severed head. That shock value is used to strike fear in enemies and ensure obedience.