Ray could have been brought to the Island as a child during the heyday of the DHARMA Initiative, much like Ben, he seems to be the right age to have been a child/young adult during the '70's-'80's.
Ray's face was cut a second time in the exact spot as his first cut, thus necessitating that it be re-stitched. At some point after that, his throat is slit and he is tossed overboard.
If you look at the picture of Ray just before he is executed on Day 99 (http://www.lostpedia.com/wiki/Image:RayBeingKilled.png), you will see that the wound has no evidence whatsoever of stitches. This is consistent with how it looked 3 days earlier on Day 96 (http://www.lostpedia.com/wiki/Image:Ray.jpg), where the wound did not have stitches then, either. So what probably happened is that on Day 94 at some point after Frank brings a satellite phone to Desmond, the doc receives the wound. The wound is most likely stitched up that same day. Then 2 days later on Day 96 the doc's stitches are removed just before he appears to take Sayid and Desmond to see the captain. Generally, stitches for facial wounds are removed after 3-5 days, so having them removed after 2 days isn't totally out of the question. Then 3 days later on Day 99 the doc is killed and his body tossed into the ocean. Then as his corpse crosses the island's barrier it goes back in time 2 days to Day 97, where it eventually drifts ashore on the island. But not only has his corpse gone back in time, but it has physically reverted to the state it was in when he still had stitches. That last part sounds totally strange, and we don't have any other instances of this happening on the show, but the evidence seems to point to it. Knowing the inherent weirdness of the island, something like that would not be completely far-fetched. It seems less likely to me that somebody purposefully pulled the doc's corpse out of the ocean, re-stitched it, then put it back in the water. I can't think of a single reason why anyone would do that.
I just realized a major flaw in that last theory of mine: when the doc's corpse washes ashore on the island, you can clearly see that his throat has been slit. If his corpse had physically reverted to the point in time when he had just gotten stitches, his throat would look normal. Now I'm theorizing that the doc's stitches were never removed and that after being exposed to ocean water for a prolonged period of time the stitches became loosened and therefore became visibly obvious. This simplifies the problem of what happened to Ray, since the scenario is reduced to the fact that his corpse simply went back in time to some point prior to Day 97, floated around long enough for physical degradation of the skin to set in, and was found on Day 97 with the stitches considerably loosened.
Ray mentions that the captain is "not a man to cross" shortly after we see the cut on his face; it was caused by the captain hitting him for a failure of some kind. You know, back when the captain was still presented as an unseen character who was supposedly really intimidating, instead of when we actually met him and discovered that he's a trembling wuss who can't stand up to Keamy.
Ray's body washes up on shore before he is killed because the island is always moving through time (forward and back) and so the time on the island is not the same time as a boat far enough offshore.