how do I turn a glass door into a removable mirror?
Specifically (without getting into product recommendations), look for "static cling film" as opposed to an adhesive product. You can get both mirrored and "stained glass" versions - they apply with water and a squeegee, and peel off again without a fight or residue. 

"Privacy film" is another search term; or "window privacy film."

The stained glass or prismatic styles will permit more light to pass while still blocking the view.

Mirrored film can have the effect of putting the "private space" on display at night when the inside is lit and the outside is dark.