In this episode (and I admit I had to look it up), the satire is about political correctness. Since the original mascot (the cow) is considered offensive by some, they have to choose a new mascot. The choices, a “giant douche” and a “turd sandwich” are infinitely more offensive than the cow, and there is the irony.
Satire is a creative genre that displays a strong use of irony and sarcasm. These are often found funny and "redeem" themselves of sorts when the content contains touchy subjects such as religion and politics. Much like what the first answer said, the South Park Cows was offensive to PETA, so they had to change their mascot. Kyle's mascot of "Giant Douche" and Cartmen's mascot of "Turd Sandwich" is definitely more offensive than cows, which is the whole point of the episode. (I'm not sure if you have seen the episode or not, but it makes much more sense when you actually watch it).