Jon wistfully recounts an erotic dream to his cat, who mocks him in return. Before we get to the nature of what Garfield is up to, consider that we cannot understand, or at least confirm, that Garfield is being a wise-ass until the punchline. The strip is built so that the strange possibility exists that Garfield is actually recounting a parallel dream that reveals his hitherto unspoken feelings about Liz. Because we know Garfield better than that, it is fairly plain that he is taunting Jon. Though the human cannot hear the cat's thoughts, were Jon to glance behind him and observe Garfield's perfect mimicry of his posture and expressions, he would likely get the gist.
Jon's moony account centers around a dream. From his speech, Jon understands dreams in the Disneyland/Martin Luther King, Jr. mode, as a sort of fond fancy which is not yet manifest in reality, and/or a shimmering goal toward which one might aspire. Whether Jon considers the dream might have any psychoanalytic weight — Freudian, Jungian, or pop psycho-spirituality — is harder to discern. He likely understands the dream as a basic wish-fulfillment scenario, but he so starry-eyed that he fails to connect the dots and read the darker implications for his waking life. Enter Garfield.
Garfield, too, claims to have had a dream. (To head off Comment section wiseacres it doesn't particularly matter if Garfield actually had this dream or not; either way, his purpose is to submarine Jon.) Garfield's dream account begins identical to Jon's, but concludes differently.
Jon finds his dream "romantic," while Garfield does not. The cat's first point is that the dream is potentially entirely meaningless. With equal possibility, we may all dream of our waking-life lovers, movie stars, nonexistent people, and mortal enemies. Garfield does not have feelings for Liz, yet had a similar dream. Dream-Liz expressing her love is not the same thing as Jon's girlfriend saying she loves him in waking life.
Garfield both denies and and supports the argument for the wish-fulfillment dream (he is a cat toying with his prey, after all). We know it is unlikely that Garfield yearns for Liz's love, because we have deep knowledge of Garfield's character: his stunted empathy, displacement of libidinal energy onto food, a sadistic streak, etc... And, informed by that jumbled pathology, that is exactly how Garfield's dream plays out. Garfield's gluttony, pride, predatory instinct, hedonism and showboating converge in a dream of excess, power and consumption of another life. By placing his own fantasy next to Jon's, Garfield parodies Jon's desires, and also implies that he dreams bigger and better than his owner.
Dozens of mammoth carcasses in various states of preservation have been discovered over the last several centuries; the flesh has always been far too decayed, reeking and foul for consumption. Should a housecat attempt to eat of these specimens, he would likely become seriously ill. Other than these museum-case sources, Mammuthus primigenius is long extinct and unavailable for hunting or meat harvest.
Finally and most importantly, Garfield is illustrating to Jon that we dream of those things that are simply, completely, utterly, forever impossible in the real world. Among those things, says Garfield, is human love.