Cut the Cheese

This phrase came from a literal source. Some cheeses, like Limburger, are so smelly that even slicing the cheese will cause its odor to diffuse over a broader area.  In other cases, the rind masks the odor of a cheese, but cutting the rind will cause the cheese to release its natural odor. (source)

Figuratively the phrase means farting because, as the source says so well, like cutting a smelly block cheese, a fart can suddenly cause a smelly odor to broadcast over a wide area.