Also known as contextomy, the fallacy of quoting out of context occurs when an original phrase is distorted or a claim is misconstrued from its original meaning, by quoting it out of context.
"One of the finest things ever done by a mob was the crucifixion of Christ. You see what I would have done is shipped him to Rome and fed him to the lions. They could never have made a savior out of mince meat."- Ben Hecht.
This is an example of contextomy because the excerpt is from a novel and spoken by a fictional character. Thus quoting this section as if it was an opinion held by the author Ben Hecht, is not an accurate reflection of the author's personal beliefs, but rather of the character who spoke it in his novel.
A few books to help you get a real handle on logical fallacies.