I know that beheading is a very old practice of execution. It is mentioned several times in the Bible. I agree that it is a tool of terrorism that goes way back even in Islamic law to the time of Muhhamad and even before Muhhamad.
What I am wondering and have not been able to find any information on and may never be able .... In the Bible the symbolism of the body is used to describe the Body of Christ with Jesus Christ being the head. Such symbolism was used many times throughout ancient culture. Do you see where I'm "heading" here? (sorry, couldn't resist the pun)
The article reference is long, I know, but it does go into the practice with the Roman's. There may be no other symbolism. Was there symbolism to crucifixions? Upside down crucifixions? It just may be how antiquity executed.
That is what most historians think. It is said that there was always a sword or axe handy and it was the simplest method available to them at the time.