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1.
The repeated use of quotes out of context in order to skew or contort the meaning of a passage or speech by an author on a controversial subject.
Conservatives have a reputation for quote mining and other ways of taking things out of context.
by The Return of Light Joker January 27, 2009
 
2.
Taking quotes out of context or misquoting someone.
"Yes, the fingerprint could belong to him, but it was of such poor quality that I cannot be sure."

...

"In his testimony he stated the the fingerprint belonged to the defendant."

"You're quote mining!"
by GuyWithCable August 12, 2008