The point of trying to work to clear you mind is not the same as when you clear your head with rest. The reason we do the later is to actually be able to rest. The point of the former is simply to clear our heads, to get away from the thousands of things running around in our head, our ideas, our problems, our tasks and so on.
Having a clear head for a part of the day for me is essential to be able to work and to be able to rest later on. If my mind wanders and races all over the place during all day my head starts to hurt, I become exhausted, I burn out well before the end of the day.
Sitting down and having to concentrate on one thing makes your head relatively clearer, you can be free from all the clutter running around in there. So my point is, that if you enjoy what you do and you want to get away from it all for an hour, perhaps you should actually sit down and work.
Sometimes I spend this time not really getting things done, but to do some organization. I organize my emails, I clear out my contact list, I plan some posts in advance, and so on. I can sometimes have fun doing this, finding new tools for the job and so on, so you don’t always have to do the hard work.
This is just an alternative to resting, if you have trouble clearing your mind, try sitting down and doing some work, or some other task which won’t let your mind wander. typically you should do creative things, since these stimulate the most of your brain. Happy working!