For the purposes of relaxing, just about anything will do, including yoga, meditation, reading, eating, drinking, and watching television.
These will not relax mind and body completely. Even sleeping in most cases can't relax your body and mind completely. The most efficient way of completely relaxing yourself is retaining consciousness while the physical body "sleeps". This is thoroughly demonstrated in yoga nidra.
The only way to completely relax the body is death. The only way to completely relax the mind is brain-death. Think about it for a minute. If the body completely relaxes, the respiratory and cardiovascular systems stop. You could hold that up for a few minutes before actually dying I suppose.
Relaxing the mind is a metaphorical idea. In context, it means thinking less (And taken to an extreme with yogic tendencies, can lead to the idea of "no-thought."). Being completely unconscious involves less thinking than being conscious, or partially conscious. Thus, "retaining consciousness while the physical body 'sleeps,'" would involve relaxing, though not completely, the body, and to some extent relaxing the mind.
A bit further though, why is complete, or near complete, relaxation desirable? What purpose is there to such a way of being? I am inclined to say that relaxation is only beneficial if one is stressed. There is a middle point that is ideal, a balance between being overly relaxed, and overly stressed. Some amount of stress is desirable. Stress inspires action, relaxation inspires inaction. One could think of each begetting offspring unto their own kind.
If one is overly stressed, they will be quite active, in fact so active so as to be detrimental, sometimes one needs to let things be. You can see this in "snappy" behavior involving over reacting to a slight stimulus. If one is overly relaxed, they tend to do little. Such people are "under-achievers." They are satisfied with what they have, and are perfectly willing to lay down on the job. "No worries man. It's all good! Chill, relax, mellow out." An excess of either stress, or relaxation, is not beneficial.