Sheogorath was turned into the one thing he hates and that's mortals.So technially a deadric prince can die.
No, the one thing he hates is predictable order. In other words, Jyggy. Sheogorath, with his insane mind, hatched a plan to perform one the most unthinkable of things, use a mortal to become him. Mortals have the gift of freedom, thanks to Shor's divine mercy, and Sheo needed that kind of freedom to break the predictable cycle once and for all.
The old Sheogorath is dead, but the new Sheogorath has always been. Sheogorath is dead, long live Sheogorath!