To sort out the significance of the mirror’s symbolism in Through the Looking-Glass, think about how the symbolism of the mirror is reflected in other elements of the text.
At first, the looking-glass (i.e., the mirror) symbolizes a kind of punishment. When the kitten disobeys Alice and doesn’t fold its arm as Alice asked her, Alice holds it up to the looking-glass so that it can see how sulky it is. According to the narrator, Alice does this to the kitty in order “to punish it.”
If the mirror symbolizes punishment, it’s possible to argue that the language, imagery, and illustrations reflect the punishing nature of the mirror. Indeed, the world inside the mirror is far from a peaceful, harmonious place. Alice regularly gets into tiffs and trouble. Whether it’s on a train, on a boat, or in conversation with Humpy Dumpty, the inhospitable language and imagery seem to tie back to the original idea that the looking-glass is an unpleasant object.
The illustrations, too, arguably reflect the notion that the mirror is a symbol for punishment. John Tenniel’s original drawings could reasonably be described as unsettling. The stark back-and-white palette, along with the haunting shading and proliferation of marks, support the idea that the world inside the looking-glass is a scary place that one visits at their own risk.