Discard chili stems and seeds. Rinse chilies, put in a bowl, and add 2 1/2 cups boiling water. Let stand, mixing occasionally, until chilies are limp, 8 to 10 minutes. Drain chilies, reserving 3/4 cup soaking liquid; discard remainder.
In a blender or food processor, whirl chilies, reserved soaking liquid, onions, and garlic until smoothly puréed.
Pour oil into a 5- to 6-quart pan over medium-high heat. When oil is hot, add beef and pork, 1 layer at a time; stir often until browned on all sides, 5 to 7 minutes per batch. As meat is browned, transfer with a slotted spoon to a bowl. Discard any fat in pan.
Return meat and accumulated juices to pan; add chili mixture, cumin, 1 teaspoon salt, 1/2 teaspoon pepper, and beer. Bring to a boil over high heat, stirring frequently. Reduce heat, cover, and simmer, stirring occasionally, until meat is very tender when pierced, 3 to 3 1/2 hours. If sauce is thinner than you like, uncover and simmer until reduced to desired consistency, 20 to 30 minutes longer. Season to taste with salt and pepper.
Nutritional analysis per 1/2 cup.