Surgeons don't "know" when people die on the operating table. All they can do is look at the signs - the pulse, the instruments, the body temperature, the breath etc. When experience tells them that any further resuscitation is likely to be useless then the theatre staff will agree that the time has come to stop. No magic departures or golden c(h)ords.
I've attempted to resuscitate a guy who dropped in the street (I had to push aside a crowd who just looked down at the guy, doing nothing). I couldn't feel a pulse, but that means nothing - pulses are often hard to find. He wasn't breathing so I tried the kiss of life, and chest compression to no avail. The ambulance arrived and they picked him up and carried him off. I didn't know whether he was dead. I never found out whether I'd helped - I rang the hospital, but they wouldn't tell me anything.
Somebody'd also stolen my shopping while I was trying to help the guy.
That wouldn't stop me doing it again, though - this life is all that we know we have. Anything else is conjecture based on very dubious evidence - read "The God Delusion" by Richard Dawkins to find out how much bollocks has been said and thought over the centuries by people with no evidence.
There's nothing wrong with death - I've been dead for billions of years before being born, and I don't remember a thing about it. When I die I have no reason to believe I'll know anything about that either. Neither will you...
So have some fun and forget about it.
Cheers
Ray