The primary concern with clipping the nails too short and cutting into the bloody tissue is that you are risking infection. Captive conditions are, unfortunately, much more "bacteria laden" than what would commonly be encountered in the wild.
I have seen wild turtles get their limbs cut off without bleeding out. Could a toenail bleed out?...possibly, but very unlikely.
The nails of my desert box turtles tend to overgrow. None of my other varieties seem to have this problem. When I cut them too short (and this happens to at least one nail on one turtle each year), I dab it in neosporin and keep a close eye on it. That's all.
Make sure to use the old style of nail clippers designed for cats and dogs. Human clippers can crush the nails. You can also use a rotary tool, which minimizes the risk of cutting into the blood vessel.
Good luck.