In reality, humans do not need to go too deep into the ocean before their blood turns blue.
Human blood is red, but in certain circumstances, such as underwater, it can appear green. The reason behind this phenomenon is similar to why deep-sea fish in the Twilight Zone of the ocean often appear red.
The explanation for this occurrence is quite simple. If you remember from your science classes, any object we see is due to the light reflected from it entering our eyes. Objects that are red appear red because they absorb other light wavelengths and reflect red light.
This is what people are taught as children. However, the reality is a bit more complex as objects typically reflect a range of light wavelengths. Blood absorbs most colors and primarily reflects light in the red spectrum. However, it also reflects a significantly smaller amount of green and blue light.
The green blood of a diver bitten by a Moray eel at a depth of about 20 meters (65 feet) underwater.
Meanwhile, water appears slightly blue because it absorbs a significant amount of red light wavelengths. If you go deep enough into the ocean, the red light is absorbed sufficiently that only blue light reflects back to your eyes, making it appear green. Thus, at ocean depths, human red blood can look green.
Because red light is absorbed very well by water, many fish that live at these depths tend to be red. At such depths, these animals are nearly invisible.
While black animals absorb all available light colors, red animals also appear black due to the lack of red light to reflect, and their bodies absorb all other available light wavelengths. Therefore, in the deep ocean, red and black animals dominate.