When you force someone in authority out of office — a politician, a king, or a cheerleading captain — you depose them.
The word almost always associated with an act of deposition is coup, meaning a sudden act of overthrowing of the government. Sometimes bloodless, more often not. On a less dramatic scale, lawyers depose less exalted folk every day; it means they take evidence from them under oath, possibly to be used in a court case later. Often those giving evidence (mobsters, murderers, financial scammers, etc,) are unwilling to talk to lawyers, hence the suggestion of a stripping away of power and dignity implicit in the term depose.