Quite simply, we can’t. All of our cells depend on oxygen in order to turn food into energy and get rid of waste. The reason that its so important to do CPR on someone who has a cardiac arrest is to keep oxygen in the blood and to keep oxygen-containing blood flowing to the brain. We can’t live without oxygen, although it is possible to synthesise oxygen, for example, in hospitals or for diving/climbing at high altitudes.
Our blood contains some extra oxygen as a kind of emergency spare, so we could survive for a while without breathing it, but I wouldn’t recommend experimenting with that!