Most mirrors don't need cleaning often. Dust that appears thick will not affect the image very much, unless you are trying to wring the last few photons out of it. I clean mirrors about twice a decade, if that.
If you read up on collimation, you can get the mirror back to where it makes good images. When you take the mirror holder out, be sure to mark the direction and position of everything first. You might just get it back together right.
Telescope mirrors are not hard to clean, but they are very easy to damage.
The first rule of cleaning is DO NOT TOUCH THE MIRROR SURFACE with anything solid. No cloths, no wipes, no Windex or other chemical cleaners.
When the mirror is out of its holder, put it in a bath of warm soapy water. Use dishwashing liquid, the plain kind with no lotion. Swish water across to loosen grit. Get some real cotton balls, immerse in the water, drag soggy ones carefully across the mirror. NO WIPING! Don't drag the same ball more than once, since it will pick up grit. Then rinse in plenty of fresh water. A last rinse with steam distilled water will get rid of any traces in tap water. Put the mirror on edge on paper towel to dry in air. The drops remaining will evaporate without a trace.
Hope you can reassemble all correctly. You can clean the diagonal the same way.
There is a mirror cleaning fluid that is expensive, dries to a film and peels away every bit. Or you could buy collodion fluid from a chemical supply. But it is explosive.
