Arrange potatoes and garlic on bottom of slow cooker. Place corned beef on top of vegetables and sprinkle with seasoning from packet. Push cloves into onion and add to cooker. Add enough water to just cover meat; cover and cook on low until tender, 6 hours and 30 minutes to 8 hours.
Transfer meat to cutting board and cover with foil to keep warm. Transfer potatoes to bowl and cover with foil to keep warm. Add carrots and cabbage to cooker, turn to high, cover and cook until just tender, about 30 minutes.
Slice beef across grain and serve with potatoes, carrots and cabbage.