Stir together biscuit mix and milk in a medium bowl until dough comes together; set aside.

Pour cans of chicken broth into a saucepan along with chicken; bring to a boil.

Take a handful of biscuit dough and flatten it in your hand. Tear off 1- to 2-inch pieces and drop them into boiling broth. Make sure they are fully immersed, at least for a moment. Repeat this step with remaining biscuit dough, then carefully stir soup, so dumplings are covered by broth.

Cover and simmer, stirring occasionally, over medium heat until dumplings are cooked through, about 10 minutes.