In the US, it's probably more natural and common to say: “Have you ever had a mango smoothie?” or “Have you ever tried a mango smoothie?” The follow up, “Did you like it?” then is consistent with the first question.
It's understood that ‘to have/had’ in this case means to drink.
The inclusion of ‘ever’ signifies/specifies that you're asking if the person has ever tried a mango smoothie in their entire life versus recently. If you were at a particular restaurant (or were talking about a particular restaurant), and you used ‘the mango smoothie,’ it would signify that you're talking about the specific mango smoothie sold by that store.