Place the beef chuck roast in the slow cooker. Add the sliced onion and minced garlic around the meat.
In a small bowl, mix the chipotle peppers, cumin, oregano, salt, and black pepper. Spread this mixture over the beef.
Pour the beef broth and one tablespoon of lime juice over everything. Cover and cook on low for 8 hours or until the beef shreds easily with a fork.
While the beef cooks, make the slaw. In a mixing bowl combine the shredded cabbage, shredded carrot, and chopped cilantro. Add the olive oil and remaining tablespoon of lime juice, then toss well and set aside.
Once the beef is done, shred it directly in the slow cooker and stir it into the juices. Warm the corn tortillas.
Fill each tortilla with a portion of the shredded beef and top with a generous scoop of the fresh slaw.