Cook first 6 ingredients in a large skillet over medium-high heat, stirring until beef, venison, and pork crumble and are no longer pink.
Meanwhile, stir together diced tomatoes and next 7 ingredients in a 4 1/2-quart electric slow cooker. Drain meat mixture, and stir into tomato mixture. Cover and cook on LOW 5 hours.
To serve, spoon chili into bowls. Top with cheese, sour cream, and green onions.
Note: Find chipotle peppers in (7-ounce) cans on the grocery aisle with Mexican ingredients.