I have witnessed the same behavior and found many headless sparrows in the 
yard after a grackle attack.  I have read that they feed the brains of 
other birds to their young (Yuk) and leave the rest of the body behind.  
It is supposed to contain the most protein.  I started putting out suet in 
the spring & it did cut down on the carnage in the back yard.  If you have 
ever heard a baby grackle screaming at their mother to be fed, you can 
almost understand her desperation.

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