Wear protective goggles and clothing. This will help prevent injury from glass or wood splinters while you work with the mirror and the cabinet door frame.
Unhinge the bathroom cabinet door from the cabinet. Support the door as you unscrew the hinge screws with a drill. Lay the door on a flat, clean work surface.
Inspect the points where the frame meets the mirror for adhesive glue. If you notice the glue, carefully test it to see if it still has a strong bond. Score the bond with a utility knife, and see if the mirror separates easily. If not, use a hot blow-dryer to melt the glue.
Separate the backing from the frame, and pry up the tacks holding the mirror down on the inside of the door.
Gently pry the frame pieces apart at a corner with a wood chisel or a flathead screwdriver, if the mirror is fitted inside of the frame molding.
Remove the bathroom cabinet mirror from the frame. Gently slide it out, and try to leave it in tact.
Measure the width and length of the old mirror, and inspect its thickness. This makes it easy to have the new mirror cut to the exact measurements of the old one.
Order a new mirror for the bathroom cabinet. With the measurements in hand, the new mirror should be a perfect fit.
Insert the new mirror into the frame. Slide it into the grove that supports the mirror. Secure the mirror by pushing down the staples or tacks that held it in place if it was mounted on the back of the door.
Reconnect the framing if you had to pry it apart to remove the old mirror. Apply wood glue to the join, and tack the two frame parts together with the frame tacks.