As someone who has been SCUBA diving quite a bit, I can tell you from personal experience that blood is a rather ugly shade of light green once you get below 50 feet or so. Of course it's not that the blood actually 'turns' this color underwater. Different wavelengths of light (that is, different colors) get absorbed differently by water. All of the red wavelengths in sunlight get absorbed in the first ten or twenty feet or so, but greens and blues get absorbed much more slowly. So when I'm underwater at 50 feet and cut myself, there is no red light to reflect off of my blood. There is still some green light, though, and apparently enough of the green light reflects for the blood to look green. However, if I took a flashlight down with me and shone the light on the blood, the light from the flashlight would only be going through a few inches of water, not 50 feet. So while there wouldn't be any red light from the sun, there would be plenty of red lights from the flashlight for the blood to reflect, and the blood would look red.

In case you're wondering, the blood I saw was from a cut I had given myself earlier in the day before I went for a dive -- there wasn't a shark attack or anything!

Thanks for an interesting question!