Brought up breakfast cereal, bypassing the beginning of stomach and small intestine (5)
I believe the answer is:
ileum
'small intestine' is the definition.
(ileum is a kind of small intestine)
I can't explain the rest of the clue.
(Other definitions for ileum that I've seen before include "Part of intestines" , "Part of digestive system" , "part of the gut" , "Food processor" , "Part of canal" .)