Phil Harrington gives a  detailed step by step instruction on how to clean reflector mirrors in "Starware".
What Qazaq said about gently blowing the dust and using a camel hair brush is sound advice.(Bear in mind, he said,"gently.")
The aluminum coating on the mirror is extremly soft and scratches with even a light touch. I know because I destroyed the secondary mirror in my 4.5 Meade reflector when I cleaned it with windex and a piece of tissue paper. I was new to astronomy at the time and I thought they were regular mirrors. You live and learn.
The dust on your mirror is most likely glued to the surface with dried moisture and contaminants from the air.
Take it out and soak it in warm distilled water(tap water contains minerals) for awhile to loosen the particals, then rinse it and repeat as many times as needed. By all means, do not try to wipe it off with any type of towel or anything like that. The loose particals will scratch the coating.
After you have cleaned the mirror, stand it up on it's side and blow the water off with a bellows. An air compressor may blast it with more moisture and oil. A hair dryer will dry the water on contact and leave deposits.
And blowing it dry with your mouth isn't recomended because you will cover it with little deposits of spit. The idea is to move the water off the surface without drying it to it.
So the best thing to use is a bellows which can be purchased at any of your local bellows stores.
Or, you can go down to your local drug store and buy a ear cleaning kit for about $5. They come with a good sized rubber bellows, and you can clean your ears too!