The experiment that Stanley L Miller and Harold C Urey conducted regarding the origin of life from inanimate matter was conducted in the absence of oxygen over water. But doesn't water contain oxygen?

Water contains oxygen. The Miller-Urey experiment used some water and was energy activated using some electrical discharge intended to simulate lightning conditions, believed to induce reactions in the inanimate matter used to produce chemical reactions that created compounds believed to be consistent with what were needed to form a complete initial organism.

The electrical discharge, if intense enough, is sufficient to induce electrolysis, which separates water into H and O, but the amount of O produced was not large enough to fundamentally negatively affect the experiment. Nevertheless, the experiment used the wrong basic inanimate matter, principally the atmosphere, and did not produce the essential compounds to show viability in creating the conditions for the origin of life.

For giving you understanding; we need Free O2 but Oxygen is also available in H20 right why dont we use it!

As the early atmosphere was reducing as there was no free oxygen but it was later produced by chemoautotrophic bacteria! Living thing release O2 in atmosphere thus making it oxidising in nature and then life evolves!