A tennessee mouthwash is any drink containing any amount of tennessee whisky.
Dude 1: "Dude what are you drinking?"
Dude 2: "Jack Daniels and Coke aka a delicious tennessee mouthwash!"
Mixed in a shot glass, Tennessee Whiskey and a cumshot.
She’s so fine, I’d like to take her home and give her some Tennessee Mouthwash!