Well, as it is right now, the Romanian version of the question represents a choice between "a cup of tea" and a "cup of coffee" and could be expressed as "o ceașcă de ceai sau o ceașcă de cafea?". Eliminating the redundancy of having "ceașcă" appear twice, you still need to keep "de" in front of the second option; dropping it is a very common mistake among native speakers.
However, the question "O ceașcă de ceai sau cafea?" could be correct, when coffee is not necessarily served in a cup. You could use the indefinite article (o ceașcă de ceai sau o cafea) - here "o cafea" has the meaning of "a serving of coffee", which might be a cup, a bottle etc.
This second version seems to be the most direct translation of the English sentence. The original sentence is more like "A cup of tea or of coffee?" (which, to my shame, I don't know if it's a valid way of phrasing it in English).