Put chuck roast into the crock of your slow cooker; season with chili powder, cumin, salt, and pepper. Add beef broth, onion, green salsa, green chiles, chopped chipotle peppers, and garlic to the crock.
Cook on High for 5 hours (or on Low for 7 to 8 hours).
Shred the beef in the slow cooker using 2 forks; continue cooking on High for another 15 to 20 minutes.