If we put ice cubes in the water, it disappears. Why?

The ice cubes don't disappear; they change form from solid water to liquid water.

They are both clear(hopefully).
Leave it in their a while and it will REALLY disappear.
I think I saw a movie where they had diamonds in water(a clear liguid?) and the clear diamonds dissappeared.

Leave it in their a while and it will REALLY dissapear.
Then the water becomes the gas form.

A solid is invisible in a liquid if their refractive indices are equal. There are solution mixtures that are used in glass labs to distinguish between Pyrex and soft glass, and other mixtures to identify gems and minerals.