Sorry but your premise is wrong. Beheading is not why anyone considers Saudi Arabia to be a barbaric country. There are so many reasons to consider Saudi Arabia a barbaric country I hardly know where to start. But I'll give it a shot:
- They execute women for witchcraft.
- They execute women and men for adultery.
- Every single one of the 9-11 terrorists were Saudi nationals.
- They practice a medieval and violent form of Islam called Wahabism.
- They expend hundreds of millions of dollars to export their violent form of Islam worldwide.
- They whip women publicly for the crime of being rape.
- They are so hateful and xenophobic that if you are not Moslem, you literally cannot set foot in many areas of Saudi Arabia.
- They are ignorant, and have no world class universities. If they need someone to do coding or mechanical engineering they have to contract those people from outside the country.
- In 2002 Al-Riyadh, the main newspaper in Saudi Arabia, published an article by a prominent surgeon claiming that Jews use non Jewish blood in Purim pastries: Blood Feast
- Women in Saudi Arabia can be incarcerated for driving a car.
- They have religious police that follow all the citizens around and can impose corporal punishment for a man and a woman standing too close to each other for example.
- Female genital mutilation is common in Saudi Arabia: Prevalence of female genital mutilation by country
There are many more reasons to consider the Saudis barbarians, and I have only touched on the most glaring and obvious points.
Trust me, beheading is the least of the reasons to consider them barbarians.