throat cut - missed voice box?`

In order to talk, they'd have to be able to push air through the larynx. A shallow cut could miss the larynx and they'd probably be able to talk. You could get the veins and not the larynx, but getting an artery without the larynx would be more difficult. That said, you could still bleed to death from a shallow, vein-slashing throat cut.

Even if you go over or under the larynx, remember not to cut into the air supply (primarily the trachea), or the air will take the easy route, out the cut, rather than being forced out through the larynx.

It was a favored execution tactic for certain Yakuza to kill with a slash to the throat. They'd cut down the throat, from ear to chest, with a katana or wakizashi (long or short sword), severing the carotid and making a huge mess. That was the point in fact, that it would splash out and make that mess. It was flashy and intimidating. Its incidental, but doing this you'd miss the middle of the neck, and thus, the larynx. Too easy. Could make for a rather dramatic death scene yes.