Clue: Cat nearly pulled back up (10)
Answer: HEAVENWARD
Explanation: Cat nearly pulled back up (10) 
HEAVE + <+DRAWN
 
One definition of HEAVE is "retch" and, something I only learned today, to cat is to vomit, therefore "cat nearly" = HEAVE. As HEAVE also means "vomit" the nearly could be considered superfluous.