[What a fabulous question! I really enjoyed thinking about this, . . . and it took me a long while to formulate my answer as a result! I originally thought Tom would be the main culprit but then I couldn't think of a single example. Honestly, I hope some other teacher figures out some further examples to add to the rich content here. This being said, my answer follows.]
Jordan Baker can be accused of sarcasm more than any other character in The Great Gatsby, but even Daisy can be guilty of it from time to time. Sarcasm, of course, is the kind of humor that is ironic and involves saying the opposite of what one really means. It is often bitter, cutting, and meant to taunt its target. Daisy is only sarcastic when she is giddy and safe within Gatsby's arms: when her mind has no fears and she is unconcerned with Tom's watchful gaze. A good example would be Gatsby's party when Daisy is happy only when she is in Gatsby's arms. Nick comments about this in Chapter 5:
Then they sauntered over to my house and sat on the steps for half an hour, while at her request I remained watchfully in the garden. "In case there's a fire or a flood," she explained, "or any act of God." (107)
What Daisy really meant, of course, was "in case Tom wanders over here and catches us in the act." Even though Tom is absent, Daisy's comment is meant to taunt him, as does her next comment when Tom finally does find Daisy at the party and asks if he can sit with a different group of people:
"Go ahead," answered Daisy genially, "and if you want to take down any addresses here's my little gold pencil." (108)
Ha! In other words, Daisy is flippantly giving Tom permission to ogle at other girls just as Daisy is now free to ogle at Gatsby. Tom has no intention of doing this (considering his attachment to Myrtle), so this comment is meant to taunt Tom directly.
Jordan Baker is full of sarcasm through the whole novel. Probably the best known example is Jordan's conversation with Nick about driving. Nick is honest with Jordan, calling her a "rotten driver," while Jordan drips with sarcasm:
"I am careful."
"No, you're not."
"Well, other people are," she said lightly.
"What's that got to do with it?"
"They'll keep out of my way," she insisted. "It takes two to make an accident." (59)
Jordan always gets a rise out of getting a rise out of people, and Nick is no exception. Her sarcasm is designed to get the careful, honest Nick angry. Jordan, of course, succeeds. Nick even refers to this event as the main reason for their eventual breakup. There are also smaller examples peppered throughout the novel, such as the conversation with Tom and Nick right before the group was about to leave for New York City with Gatsby and Daisy:
"I've made a small investigation of this fellow," [Tom] continued. "I could have gone deeper if I'd known--"
"Do you mean you've been to a medium?" inquired Jordan humorously.
"What?" Confused, [Tom] stared at us as we laughed. "A medium?" (122)
Again, here's a joke meant to taunt Tom, who would never have consorted with someone so low-class as a fortune-teller over his hatred for Gatsby. There's always something like this coming out of Jordan's mouth. This both endears her to Nick as well as disgusts him. Jordan fascinates Nick, as she doesn't seem to fit into the mold of a traditional woman; however, she works quite well with the new Roaring Twenties image of a flapper. Either way, sarcasm is Jordan's strong-suit.