Combine first 7 ingredients in a small bowl; stir well. Cover and chill.
Leave root and 1 inch of stem on beets; scrub with a brush. Place in a medium saucepan; cover with water. Bring to a boil; cover, reduce heat, and simmer 45 minutes or until tender. Drain and rinse with cold water. Drain and cool. Trim off beet roots; rub off skins. Cut beets into 1/4-inch slices.
Arrange beet slices on each of 4 lettuce-lined plates; top each serving with 1/4 cup salsa.