To give someone the moon door means to break up with somebody. Alternatively, it means to fire somebody from a job.
Basically, the word describes any situation in which someone's position or status is completely stripped away from them in one fell swoop.
This phrase derives from the book and TV series, Game of Thrones, in which there is a castle on a high mountain with a hatch built into the floor. This hatch is called the "Moon Door." When opened, the Moon Door releases people into mid air, so that they fall directly to the floor of the Vale far below.