How do I get rid of the little cirlces that my mirror's suction cups have put on my shower wall?

Because of the lower pressure in a small area, the atmospheric pressure outside pushes down on it and holds it firmly in place. Suction cups will hold on until either the cup is lifted from the side allowing air in and makes pressures equal or by applying a force large enough to overcome atmospheric pressure. http://www.kingfar.com.hk/Suction-Plasti...

Indeed. It relies on negative fluid pressure of air (or water) to adhere to nonporous surfaces, creating a partial vacuum. The force needed to pull it apart is determined by the area of the cup and the pressure (typically normal atmospheric pressure).

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