Set a steamer basket in a large saucepan with a lid. Fill with enough water to come just below basket; bring to a boil. Place beets in steamer basket, cover pot, and reduce water to a gentle simmer. Steam until beets are tender, 30 to 35 minutes. When cool enough to handle, grab beets with a paper towel and slip off skins. Cut the beets into thin slices.
In a medium bowl combine sliced beets, garlic, vinegar, and oil; season with salt and pepper and toss to combine. Cover and refrigerate several hours or overnight. Remove and discard garlic. Serve beets topped with mint and goat cheese.