Lord Capulet, none too pleased to learn that his daughter is refusing to marry Paris, calls Juliet a "mistress minion", a "green sickness carrion" and a "tallow face." This is a very interesting question, because its explanation requires some knowledge of the superstitions of Renaissance thinking.
Mary Fissell, in her article "Girls in Green," explains the meaning of being threatened with "green sickness":
This worrisome condition was caused by the cessation of menses. Contemporary medical theory reasoned that the stoppage of menstrual blood led to dire consequences, since menstrual blood was full of harmful substances that the body sought to expel. Young women with this ailment turned a delicate shade of green or white because blood left all other parts of the body and converged in the womb or liver.
Being called "tallow faced" was not nice either (of course). Tallow is the fat of animals used to make fat or soap. Perhaps calling name was to make her feel ugly (so why would she reject such a good match?)
As for "mistress minion" one would need to consider the archaic definition of "minion" which was "one who pleases rather than benefits." Lord Capulet is being very sarcastic....he's essentially calling Juliet "baggage."