As another noder
pointed out, the trick is to kill the virus
, not tear/burn/slice/freeze your own skin off.
The best method I've found for doing this is plain old raw garlic. I've tried it several times on various people, for skin tags as well as warts and plantar warts, and not only does it work really well, there's a really low recurrence rate -- that is, neither myself nor any of the other guinea pigs ever had one come back that I know of.
I call it "The Garlic Slab Cure". Garlic, as you probably know, is quite powerfully antibiotic, antifungal and, for all we know, anti-alien-bodysnatch. So what you do is, take a clove of garlic, peel it, and cut it in half shortways. Take from one of these halves a cross-section, making the closest thing to a coin-shaped slice or, as we say, a slab.
Slap the slab on the wart, and trim off the extra -- you don't want garlic on your bare skin for very long; it can actually leave a burn. Put a band-aid over that and leave it on for either one whole day or one whole night--about 10-12 hours total. Then take it off, and let it air for the next 10-12 hours; lather rinse repeat.
The wart will get red and irritated after 1-3 days, and fall off in 5-14 days (depending on the size and depth of the problem). It will bleed a little, but probably not leave a scar, and there's almost no chance that it'll become infected, since you've had an antiseptic on it the whole time. And as I said, since this kills the virus in your skin that caused the thing in the first place, it's highly unlikely that it would ever come back in that location--though, if you're prone to warts for whatever reason, you may get them in other locations, of course.
Duct tape works by almost the same principle, except instead of being germicidal, it kills the virus by depriving it of oxygen. In cases where this doesn't work (some wart germs are anaerobic, and sometimes some air can leak in), garlic is a good option.