Firstly, Sauron did not die, ever. He is neither an elf nor a mortal, rather he is a Maya, sort of the equivalent of a Greek lesser God. Even when Frodo finally destroyed the Ring, Sauron still lived.
Sauron has however seemed to perish before by going to the Abyss when Numenor fell and then coming back, though less powerful than before. As Gandalf described it (paraphrasing), once the Ring were destroyed, Sauron would be reduced to a shadow gnawing at itself in the dark. Dead to this world for all intents and purposes, but not technically.
So if it is a question of what happens to Sauron's physical form once he wrestled with Gil-Galad and Elendil and had his finger cut by Isildur, there is nothing that Tolkien wrote that goes to specifics as to whether his body remained intact, conscious, turned to ash or what.
One thing that is stated in the FOTR is that Gollum after having been captured and personally tortured by Sauron described him as having nine fingers. This suggests that the physical act of Isildur cutting Sauron's finger had a lasting effect. So either Sauron's body remained somewhat intact (conscious or otherwise) or was disintegrated and then reconstituted with a missing finger.
As Gandalf is also a Maya, (but of a lesser order to Sauron according to his own words), Gandalf had fallen in battle against the Balrog, but was somehow brought back to life. Again it's not made clear whether Gandalf's body maintained a physical presence through the process, or if Gandalf was temporarily non-corporeal. I personally imagined the former and feel the same is true for Sauron.