Source: A search for "how to flush the toilet when" and looking at the language used in the results. It seems like "off" is the most common, but there are some variations:
I would say not working if it's broken. If someone asked for a drink: "Sorry, our water isn't working."
In some cases I might say broken, but you risk having a haha moment because "broken water" is a stage of childbirth. But I might say, "The ---- water is broken again!" to the landlord. I'm also more likely to use this for hot water specifically, "Don't take a shower, our hot water is broken." If you want to be fancy then you can specify what's broken--the pipe or the hot water heater or whatever.
Off has an implication that it was turned off deliberately. Usually a broken pipe will also result in the water being turned off but the water could be turned off for other reasons, too (like if the pipes are being upgraded). If I used this, I would probably be more specific: "Our water is off while the city repairs the pipes."
Cut off means that someone else turned it off outside your control. This has a slight implication that it was turned off for non-payment unless there's some other context explaining why it was cut off.
Out sounds like British English to my (American) ears. I would probably understand it, but I probably wouldn't naturally say it that way.