Fetching details from the dictionary...

to breathe out; to breathe
to tell (a lie); to use (foul language)
to vomit; to throw up; to spit up
深いため息をつくと少し気持ちが楽になった。
I felt a bit better after letting out a deep sigh.
冬の寒い朝は白い息をつきながら歩く。
On cold winter mornings, I walk breathing out white puffs.
最後の一息をつくまで挑戦し続けたい。
I want to keep challenging myself until my last breath.