Combine smoked paprika, garlic powder, onion powder, salt, and black pepper in a small bowl.

Rub the spice mixture evenly over the beef chuck roast.

Place the seasoned roast into a slow cooker.

Pour the beef broth and apple cider vinegar around the base of the meat.

Cover and cook on low for 8 hours until the beef is tender and shreds easily.

Remove the meat from the slow cooker and shred it using two forks.

Return the shredded beef to the slow cooker, stir in the sugar-free BBQ sauce, and heat for an additional 15 minutes before serving.