Mixing Gatorade with alcohol would just create a juice cocktail. Gatorade, although a sports drink, is a juice.
There are several drink recipes available through online sources such as the Make Me A Cocktail website that have juice cocktails readily accessible. Users simply input the requested ingredient in its search engine. Some common pairings with Gatorade include Gatorade and whiskey, Gatorade and vodka, Gatorade and gin, Gatorade and coconut rum and Gatorade and rum.
Juice cocktails are made from just about any noncarbonated beverage. Many people prefer to mix higher proof alcoholic drinks with sweet juices as it is easier to swallow.