In Fellowship of the Ring it is shown that Isildur cut the finger which holds the One Ring from Sauron's hand. But at that time, Sauron was very powerful because of his wearing the Ring. So how could a mere man cut Sauron's finger with a simple blade when Sauron was most powerful?
But at that time, Sauron was very powerful because of his wearing the Ring.
The One Ring did not make Sauron stronger; he simply poured his spirit and malice and will to dominate into it; think of it like a horcrux, if you are familiar with the Harry Potter universe... you have to destroy the ring before you can truly defeat Sauron. At best, this was an implement; a tool, used by Sauron to direct his will. It enabled him to be more effective at dominating and influencing other peoples by way of establishing dominion over most of the other magical rings of power, but it did not make him more difficult to beat in a sword fight, or harder to cut with a sword.
So how could a mere man cut Sauron's finger with a simple blade when Sauron was most powerful?
To begin with, Isildur was a Numenorean, and the son of Elendil. He is descended from Elros Half-Elven, and from Fingolfin, who did battle with Morgoth himself, and smote him many times. While Fingolfin was defeated, he left Morgoth with a permanent limp when he stabbed Morgoth in the heel. That is to say, Isildur is no 'mere' man.
If Fingolfin could permanently injure the greatest and most powerful of the Valar (basically gods), then perhaps you can see how a descendant (though far removed) could also injure a lesser being such as a Maiar (essentially a demigod). Remember that Sauron was simply Morgoth's 'chief lieutenant' (and not even the first being to be so), not necessarily the most powerful, and he is certainly not invincible.
Consider all the peril that Gandalf finds himself in during his recorded tales in Middle Earth; he is a Maiar like Sauron, and yet seems quite taxed after doing battle with 'mere' orcs and goblins and trolls, nearly falling prey to them on several occasions.
Also consider that aside from Isildur, Sauron was doing battle with Gil-galad (officially the chief among Elves in Middle Earth at the time, and perhaps most powerful, if you discount Glorfindel and Galadriel) and Isildur's father, Elendil himself. Only after Sauron barely defeated Gil-galad and Elendil was Isildur able to cut the ring from Sauron's finger. Had Isildur entered into combat with Sauron first, and/or alone, he almost surely would have been slain.