Heat a large skillet over medium-high heat. Cook and stir ground beef in the hot skillet until browned and crumbly, 5 to 7 minutes. Add hoisin sauce and peanut sauce; cook until heated through, 2 to 3 minutes.
Spoon beef mixture into the center of lettuce leaves, taco-style. Top with cucumber, carrot, and mint. Season with salt and pepper.