cut out vs pull out

cut out

verb
  • Used other than figuratively or idiomatically: see cut, out. To separate into parts with or as if with a sharp-edged instrument; sever. 

  • To take a ship out of a harbor etc. by getting between her and the shore. 

  • To intercept. 

  • To arrange or prepare. 

  • To remove, omit. 

  • To refrain from (doing something, using something etc.), to stop/cease (doing something). 

  • To oust, to replace. 

  • To separate from a herd. 

  • To stop working, to switch off; (of a person on the telephone etc.) to be inaudible, be disconnected. 

  • To leave suddenly. 

adj
  • Well suited; appropriate; fit for a particular activity or purpose. 

pull out

verb
  • Used other than figuratively or idiomatically: see pull, out. 

  • To maneuver a vehicle from the side of a road onto the lane. 

  • To draw out or lengthen. 

  • To use coitus interruptus as a method of birth control. 

  • To remove something from a container. 

  • To withdraw; especially of military forces; to retreat. 

  • To transition from a dive to level or climbing flight. 

How often have the words cut out and pull out occurred in a corpus of books? (source: Google Ngram Viewer )