Perhaps take up the study of a martial art. There are some forms that are "lower impact" that don't have such high probability of harming your hands if that's a concern.
Somebody said above that it's more about physical relaxation than mental relaxation. I'd agree with this (this is just what I've learned about myself) - physically, it's purely about utilizing only the muscles necessary for the movment. Economy of motion. Martial Art study goes to this end to a great extent as well where the entire body is relaxed and a strike will eminate from just around the belly button area, but every muscle inline from there to say, the ball of your foot is completely relaxed, until the moment of impact when all the force is summoned to the ball of your foot, and only the ball of your foot, as it smashes its way through a stack of boards (or an opponents skull

and immediately after the blow is delivered, everything is relaxed again. It's not obvious to folks that don't practice martial arts, but I have found so many parallels between music and martial arts as to be baffled by it myself at times.
Mentally, it's kinda two fold (I think) - you want to be relaxed in as much as you are not shaking from nerves, but you want your mind to be fully engulfed in the music you are producing, and if the music is violent and devastatingly emotional, then your mind should be inline with that. Same for a meloncholy prelude or whatever the piece may be. It's really hard, and as such I won't attempt, to explain in writing how to acheive mental and physical relaxation we're talking about here. Chang discusses the physical aspects at length in his book, though I do admit to only briefly reading those sections as it's not an area I have much difficulty with.
I am also no expert and not an advanced student, but my relaxation ability I think from martial arts is "advanced".
The one thing I will try to describe is the idea of clearing your mind so that you can then focus all of your mental energy on the necessary components for relaxation, and to do so I'll once again relate it to a martial arts experience. I was recently taking a promotion test, and I had to stand up in front of a room full of judges and family and friends and perform a "Poomse" (which is a pattern of pre-defined motions that essentially are mimicking the fighting of multiple opponents. It's essentially a choreographed performance with the quality being in the details of execution, not at all unlike a piece of classical music.) So anyway, I got up there and my mind went blank. Suddenly I had no idea what I was even there to do, my palms started sweating and my heart started racing. (this is exactly the physical and mental experience I had the first time I sat down to play a piece of classical music solo in front of an audience, and to an extent, is exactly the thing I experience everytime I sit down to perform!) So anyway, the first motion of this Poomse, it isn't even a "motion" so much as whats called a "ready stance" and it involves focusing your eyes on a point and slowly beginning with your hands sorta cupped open and up down at your hips and slowly bringing them up and out until they form a spade sort of shape in front of your eyes. This whole motion is coordinated with your breating. As my breath was finally exhaled and my hands were in the spade shape, all of the sudden I was completely relaxed, completely unaware of people watching me and the form I had to perform was crystal clear in my mind. I passed the promotion test.
-Paul