In Romero's zombie lore, destroying a zombie's brain kills the zombie. Merely severing a zombie's spine won't kill them. If you severed the head from a zombie, and the neck was still attatched to the zombie's head (leaving the brain stem undamaged), would it make the zombie's head dead, or would the head remain undead? Put another way: Would the severed zombie head with its neck still connected be a zombie lurker?
In Romero's films, it is as you suspected, that decapitating a zombie merely leaves it unable to walk around but it's head will still be undead. The only thing that will 'kill' a Romero zombie is traumatic damage to the brain.
It was shown in Romero's Day of the Dead (1985) that a decapitated head can still be animate:
Dr. Logan 'revives' Johnson's decapitated head.
In the 2004 remake of Romero's "Dawn of the Dead" there is a scene in the camcorder footage at the end in which the survivors find a plastic cooler in an abandoned boat. It has probably been there for weeks.
It contains a bloody severed head. The eyes still move, the jaws still snap, and presumably its bite is contagious.
Making sure I understand this; are you asking if the act of cutting off a zombies head but not damaging the brain in the process would kill a Romero zombie?
If so the answer would be no, the zombie would still be undead although it was only a head. To kill a Romero zombie you have to destroy the brain.
As an addition to Ian's answer, in The Zombie Survival Guide series which is as close to Romero as you can get (although Brooks goes into a little more detail, if I remember Romero's works correctly), you find the following story:
In order to be promoted, the apprentices in some "ancient zombie fighting order" of samurai had to survive one night in a room filled with live-zombie heads in jars that were kept on shelves on the walls of a room. The proximity (screaming? without vocal chords?) to dozens (hundreds?) of undead would apparently turn most insane in one night.
The zombie genre is very sketchy in this matter. I have seen zombies such as the rabid in 28 Days Later that cannot deal with head severing since they are technically alive. I have also seen movies and series such as The Walking Dead and the World War Z book where the infected can remain alive indefinitely with a severed head.....take your pick.