The sky can affect the color you see on the ocean surface.
But deep clear water does not look blue mainly because it reflects the sky.
Water itself interacts with sunlight in a way that favors blue.
Sunlight contains many colors
White sunlight is a mixture of visible wavelengths.
Different wavelengths correspond to different colors.
When sunlight enters water, those colors do not all travel equally well.
Red light is absorbed more strongly
Water absorbs longer visible wavelengths such as red and orange more strongly than blue.
As light travels farther through the water, much of the red disappears first.
Blue wavelengths can travel farther.
Some of that blue light is scattered back toward your eyes.
That is why a large volume of clear water can look strongly blue.
Why does a glass of water look clear?
A drinking glass contains only a small amount of water.
Light does not travel far enough through it for the color-selective absorption to become very obvious.
In the ocean, light may travel through meters of water.
The effect becomes much stronger.
Does the sky matter at all?
Yes.
The surface can reflect blue sky, clouds, sunsets, and nearby scenery.
That changes what you see, especially at certain angles.
But sky reflection is not the main explanation for the blue color of deep clear water.
Why is some ocean water green or brown?
Other materials can change the color.
Algae and microscopic organisms can make water appear green.
Sediment can make it brown.
Shallow sandy bottoms can produce bright turquoise colors.
Depth, particles, organisms, and the seafloor all matter.
Why can deep water look dark blue?
As light travels deeper, more wavelengths are absorbed and less light returns to your eyes.
The remaining light can be strongly blue until the water becomes dark enough that very little visible light remains.
So the ocean is not simply a giant mirror reflecting the sky.
The water itself is doing much of the coloring.
A related part of the natural world appears in Why is the ocean salty?, where the same kind of physical or biological reasoning answers another familiar question.
And that’s the short explanation.
Related explanations: Why is the sky blue?, Why is the ocean salty?, and Why does a straw look bent in water?