It's more about ruthless deception. Cutting the head of the snake is the worst approach.

"The first method for estimating the intelligence of a ruler is to look at the men he has around him."---Machiavelli

Control the body and turn it against the head, so you are democratically heralded as the new head. Maintaining the body of the snake requires balancing ruthlessness and kindness to keep from a tyrannical uprise.

"Any man who tries to be good all the time is bound to come to ruin among the great number who are not good. Hence a prince who wants to keep his authority must learn how not to be good, and use that knowledge, or refrain from using it, as necessity requires." --- Machiavelli