To give someone the moon door means to break up with somebody. Alternatively, it means to fire somebody from a job。
把某人推出月亮门指与某人分手，也可以指，把某人炒鱿鱼。
Basically, the word describes any situation in which someone's position or status is completely stripped away from them in one fell swoop。
这个表达的基本意思就是，一下子就把某人的身份或地位完全剥夺。
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。
这个表达来源于热门小说及改编电视剧《权力的游戏》，里面有个城堡建在高山上，而城堡的地面上有个可以打开的出口，这个出口就叫“月亮门”。这个月亮门一旦被打开，站在上面的人就会跌落到下面的深谷中。