Do you mean the mirror inside the front of the camera? If so, if the camera is under warranty I would only recommend having it professionally cleaned. That might even be a good idea if it's no longer under warranty, unless you are very confident of your own abilities. It can be "wet cleaned" similar to cleaning the sensor, but has to be done very carefully using the correct cleaning solutions and optical swabs. The mirror is "front surfaced" with vaporized aluminum, very easy to damage, and rather pricey to have replaced. Might be worth a small fee to have it professionally cleaned.
If you are seeing smears within the pentaprism (looking through the eyepiece), those are most likely on the focus screen. Once again, it's a delicate item and using the wrong things to clean it can make matters worse. 5DIII doesn't have an easily removeable and replaceable focus screen, either. It also might be best left to a professional cleaning.