[Grishnakh]

That last part isn't regeneration, it's scarring. If it were regeneration, the skin would grow back just like new. The reason we scar instead of regenerating is to reduce the chance of infection; regenerating, as many simpler animals do when injured, takes longer and leaves the wound open to infection. We opted for scarring to avoid this. As for evidence of a cut afterwards, if you look at the skin under a microscope, layer by layer, you'll probably see the evidence, though it probably depends on the severity of the injury. Anything that goes through all the layers of skin leaves a scar, to my knowledge.

As for growing new skin to replace old, the new skin we grow isn't a perfect replacement. If it were, older people wouldn't have wrinkles. We have a limited healing capacity, but it's not regeneration. Regeneration would have us growing tissues that are identical to those we had when we were young, with no evidence of scarring at all.