I'm sorry , kizanne, I hope that was a typo. Death from cutting the carotid arteries should happen in 1 to 5 seconds, not minutes!
I just finished processing 6 turkeys last week. A good, firm slice to the throat with a razor sharp knife, they were unconscious in 2 to 3 seconds and totally bled out in 5 to 6 seconds. However, that's when nerve impulses begin the automatic wing flapping. Don't confuse this with suffering! It's a convulsion, an electric storm from dying neurons. It happens without a head, too.
The turkeys didn't suffer because they never felt the cut. I know this because I held their head and watched their eyes as I did it. They just looked at me, and went to sleep! This is why a super sharp knife is so important! When you cut yourself with a sharp blade, like a razor, you barely (sometimes never) feel it. Whereas when you get cut with a dull blade it hurts like the dickens. I use a pocketknife that I sharpen so that it will shave hair, and no one feels the cut!
It is also important to cut in the right place, from behind the ear down past the jaw, and with a firm hand to cut deeply so that you cut both the jugular vein and carotid artery. You will know if you have done well because the blood comes out in a great gush, all at once. Do both sides, and let them drain for 5 minutes or so, until nothing is dripping out.
Practice makes it easier, thanking the bird in advance for their sacrifice also helps my conscience.
Good luck!
~S