Typically countries that have certain banned cocktails are those that have banned alcohol altogether. Otherwise, there are certain areas in countries that have banned specific cocktails. There are many Middle East countries that have banned alcohol so cocktails would also be banned. These countries include Afghanistan, Bahrain, Bangladesh, Brunei, and India.
There are states in the U.S. that have banned certain cocktails for various reasons. Absinthe is probably the most famous cocktail to be banned in different countries in North America and Europe. It has drastic side effects. The Nutcracker is banned in New York City most likely due to its high proof of alcohol. The Moby Dick Whale cocktail is banned in the United Kingdom but it is because of the use of the parts of the whale in the drink.