Cut the grapefruit, orange, and lime in quarters and remove the peels. Slice the apple into small segments, discarding the core. Peel the beets and cut into pieces that will fit through your juicer chute.
Feed the ingredients through your juicer in the order listed (starting with the grapefruit and ending with the carrots). If the discarded pulp is wet, run it through the juicer a second time. Stir the juice to combine.
Refrigerate or serve over ice.