Did you cut any of the veins when you cut that egg? Have you tried flushing it out with water the same temps as the egg? to see if the stain is evenly spread or a patch of bacteria or something?
How long is it since you cut these eggs?
ETA - looking at the cloudy egg pic I wonder if it didn't die earlier before you cut and is in the process of decaying - those veins look awfully thin and faint.
You can't kill the baby by cutting the membrane - but you can make it a lot easier for infections, fungus etc to get in.