What does it mean to dream you cut off a snakes head?

Dreams are meaningless ! We have on average up to twenty dreams every night - but we only remember the last one, because we're starting to wake up. Dreams are random images conjured up by the semi-conscious brain - while the body repairs itself during sleep.

Since this category is "Dream Interpretation," here is a serious answer:

In dreams, snakes can have many different meanings, ranging from dishonesty and danger to medical practice and rejuvenation. In this specific dream, the image is one of "cutting off" a problem or danger. The image relates to ancient sayings about killing a "serpent" (snake) by cutting off the head; cutting off the tail only makes the problem worse. The metaphor applies particularly well to an evil force or organization; attacking pawns or minor participants accomplishes nothing. One must destroy the "head", i.e., leadership.