Cast out, rid oneself of, as in He threw off all unpleasant memories and went to the reunion. [Early 1600s]
Give off, emit, as in The garbage was throwing off an awful smell. [First half of 1700s] Also see throw out, def. 1.
Also, throw or put off the scent. Distract, divert, or mislead, as in A mistaken estimate threw off her calculations, or These clues were designed to throw the detective off the scent. The variant comes from hunting, where the quarry may try to put pursuing hounds off the scent. Its figurative use dates from the mid-1800s. Also see off the track.
Perform in a quick, spontaneous, or casual manner, as in He threw off one sketch after another. [Mid-1700s]