Add the pork shoulder, sliced yellow onion, minced garlic, beef broth, chili powder, smoked paprika, cumin, and 1 teaspoon salt to the slow cooker. Stir to coat the pork evenly.
Cover and cook on low for 8 hours until the pork shreds easily with two forks.
While the pork cooks, place the thinly sliced red onion in a small bowl. Stir together the apple cider vinegar, sugar, and 1/2 teaspoon salt, then pour over the onion. Set aside to pickle.
In a separate bowl, combine the shredded cabbage, grated carrot, mayonnaise, and lime juice. Toss until the vegetables are coated and set the slaw aside.
Once the pork is done, shred it directly in the slow cooker and mix with the cooking juices.
Warm the corn tortillas in a dry skillet or microwave. Fill each tortilla with pulled pork, a spoonful of slaw, and some pickled onions. Top with cilantro and serve with lime wedges.