Is it "cutting off" in the pattern when I go before a plane that is going faster than I am but let me in first?
The Cheyenne would have been "cutting you off", if he hadn't worked it out with the aircraft in the pattern and maintained visual separation.

According to the AIM, 4-3-3, standard pattern entry at an uncontrolled airport is abeam the midpoint in the downwind. 


  
  Enter pattern in level flight, abeam the midpoint of the runway, at pattern altitude. (1,000’ AGL is recommended pattern altitude unless established otherwise. . .)
  


http://www.faraim.org/aim/aim-4-03-14-189.html