cough (something) up
Definition: to remove something from your stomach or throat by coughing.
(This phrasal verb has more than one meaning.)
E.g.1: If someone has internal injuries, they might cough blood up.
E.g.2: She nearly choked on her sandwich but luckily she managed to cough it up.
This phrasal verb can be separated. (E.g. 1 & 2)