What's interesting here is that the phrase has come down to us as "green with jealousy," as if that emotion had a particular color. What Shakespeare was describing, of course, was the cat. It was much more common in his day to see cats catching rodents, and cats will, in fact, play with a mouse until death, afterwards settling down to a tasty treat. So "mocking" in this useage has the sense of derision or contempt.
What's also interesting is that Iago is jealous of Othello, yet warns him about jealousy! Psychologists would call this "projection." Iago in thought and deed "plays" with Othello until he is dead. It would be interesting to go back in time to the first performance, and see if in fact, the actor playing Iago had green eyes.
Asimov's Guide to Shakespeare, Gramercy Publishing, 2003 ed., pg I-622.
Othello. Act III. Scene iii.
Iago. Oh, beware my Lord, of iealousie,
It is the greene-ey'd Monster, which doth mocke
The meate it feeds on. That Cuckold liues in blisse,
Who certaine of his Fate, loues not his wronger:
But oh, what damned minutes tels he ore,
Who dotes, yet doubts: Suspects, yet soundly loues?
Oth. O miserie