So you think Sauron was broken by Isildur cutting his finger off as opposed to Elendil and Gilgalad stabbing him all over his body?
If Isildur took Sauron's ring then Sauron would just take it back, only in this case he couldn't because he was already dead.
Hypothetical situation: Imagine Sauron with the One Ring was going about on Mount Doom and Frodo, say, snuck up and pinched it off his finger—would
that have killed him? Of course not, and the situations aren't too different. Are they?