According to mirror installation instructions in the Home Guides section of San Francisco Gate, it is possible to glue a mirror to a wall with mirror mastic, a heavy-duty adhesive that creates a permanent bond. The surface of the wall requires preparation to maximize adhesion.
Interior designers often use mirror adhesive instead of clips to glue frameless mirrors to walls. Using clips disrupts the mirror's edge flow, whereas using adhesive allows for a permanent fixture and a clean style. Although mirror mastic creates a permanent bond, the mirror can still be removed without shattering when using a hammer and a hand trowel.