Even if he's dead, he's not dead.
! I don't see Jon staying dead if he really is dead either. I don't think his body is going to live through that though. Those stabs looked pretty much fatal. Of course, if the writers want them to look fatal without them actually being fatal to trick the viewers, "Surprise he's still alive" they could do that but I don't see them going down that route. I mean, what would Dravos and Mel do with such a badly injured body anyway? They can't transport him out of the castle in that condition. They would have to hide him and nurse him back to health in Castle Black under the very noses of the people who tried to kill him.
! Not to mention the fact that the people who tried to kill him would wonder where the body went. Nah, I think he's dead and he'll either later be revived or he warged himself into another body. I guess…technically if he warged he's not dead because his spirit has inhabited another body but you know what I mean. In the end though we know his character will be back and play his integral role in the plot.
! Edit: It may not be out of reason to believe Mel can also heal serious wounds instantaneously if she's presumed to be able to revive someone from the dead.