Does John Watson die in Sherlock season 3 episode 3?

No, John Watson does not die in Sherlock season 3 episode 3. That episode is called "His Last Vow", and while it's a very intense episode with John facing a serious threat, he survives.

The episode features a plot where John is targeted by Charles Augustus Magnussen, a powerful and dangerous individual. While John is in danger, he ultimately survives the ordeal with the help of Sherlock.