Since you say "it is depicted", I'm guessing you're referring to the movie?
In the books Sauron's body dies a number of times:
- His true body, fair of face, died in the ruin of Numenor:
But Sauron was not of mortal flesh, and though he was robbed now of that shape in which he had wrought so great an evil, so that he could never again appear fair to the eyes of Men, yet his spirit arose out of the deep and passed as a shadow and a black wind over the sea, and came back to Middle-earth and to Mordor that was his home. There he took up again his great Ring in Barad-dûr, and dwelt there, dark and silent, until he wrought himself a new guise, an image of malice and hatred made visible; and the Eye of Sauron the Terrible few could endure. (The Silmarillion)
- As seen at the end of the previous quote, he constructed himself a new body which he then lost at the hand of Elendil and Gil-galad:
Sauron himself came forth; and he wrestled with Gil-galad and Elendil, and they both were slain, and the sword of Elendil broke under him as he fell. But Sauron also was thrown down, and with the hilt-shard of Narsil Isildur cut the Ruling Ring from the hand of Sauron and took it for his own. Then Sauron was for that time vanquished, and he forsook his body, and his spirit fled far away and hid in waste places; and he took no visible shape again for many long years.(The Silmarillion)
- After the destruction of the Ring by Frodo
If [the Ring] is destroyed, then he will fall, and his fall will be so low that none can foresee his arising ever again. For he will lose the best part of the strength that was native to him in his beginning, and all that was made or begun with that power will crumble, and he will be maimed for ever, becoming a mere spirit of malice that gnaws itself in the shadows, but cannot again grow or take shape. (The Fellowship of the Ring)
Isildur's removal of the Ring may have destroyed Sauron's body (though it may have also been invented by Peter Jackson as a cool visual), but Sauron fled rather than the body dying in what we would consider the normal sense.
So yes, if
someone managed to sneak up behind him and strike some fatal blows to him Sauron may well have fled his body too if he could not foresee an alternative way to escape, and yes, Sauron's body was destroyed a number of times, only one of which involved separating the ring of power from it.