Question: What is the characteristic of used water itself? If it became removing hadath, or by being used for worship - for either case?
Answer: Water becomes used by using it for prescribed worship (adab, sunnah, waajib, fard) with the intention of worship. It also becomes used by removing hadath, which would be the first wash in ghusl (after intercourse, completed menses, etc.) or wudu (after e.g. urination) without intention.
When water is used one cannot use it for ghusl or wudu, but it can be used to remove najis filth, such as blood or urine.
... and Allah knows best.