In English, "I am not having water" is a valid sentence and "to have" is often used in this way. Example in a restaurant setting: "I'm not having the chicken, I'm having the pasta."
But mít does not have the same meaning in Czech as "to have" as it is used in your sentence and in the example. The simple present is correct here.
This is already discussed in the answers to the self-deleted comment by emiliano. As ion mentions, to have can be a regular verb. We generally accept the British use of "have" as a normal verb in this course. Have you any wool? I have not wool.
This usage has indeed been strongly disappearing with time in the recent centuries. Nevertheless, people do use it in their answers and we do accept it.
Regarding "no water", we currently take it as the equivalent of "žádnou vodu". This policy may be adjusted in future.