Step away from the camera. I repeat, step away from the camera.
Mirror cleaning really needs to be left to professionals, especially if it involves physically touching the mirror with your cleaning equipment. Why? Because the mirror is on the front surface and partially silvered in places. It's highly vulnerable to damage by even minutely rough cleaning. If you manage to damage portions of the mirror surface you risk exposure and focus issues. Not worth it.
Of course, if you leave that thing stuck to your mirror you risk exposure and focus problems, so you need to have a competent repair person do a cleaning of the mirror box for you, including the surface of the mirror. Even I won't clean a mirror unless I'm in the middle of nowhere and have no alternative (e.g. can't keep shooting with it the way it is).
