Carrying out a beheading? (9)
I believe the answer is:
execution
This clue is a double definition.
'carrying out' is the first definition.
(synonyms)
'a beheading?' is the second definition.
(beheading is a kind of execution)
(Other definitions for execution that I've seen before include "Eg, beheading" , "Queen of Hearts' order" , "Topping" , "style of musical performance" , "The carrying out of" .)