Remove the staples holding the china cabinet's back panel to the sides and top. If the staples are deeply inset into the wood, a thin-bladed screwdriver is used to force the staples up enough to allow a needle nosed pliers to get access. Alternately, remove the screws holding the back panel to the frame. Place the screws in a plastic bag and label it.
Feel through the tape holding the mirror to the inside of the frame until you locate the mirror's edges.
Run a thin-bladed utility knife with just a small portion of the blade showing along the edge of the tape, loosening it from the frame. Have an assistant hold the mirror against the frame from the back while you do this.
Push on the front of the mirror from the inside of the cabinet. Have another assistant on either side of the mirror, bracing it and holding it in anticipation of it coming free. If the mirror is cracked completely through, remove the topmost piece first.
Lift the mirror from the frame as it is pushed backwards. Place it in a safe, out-of-the-way spot.