Question

Why is minister more powerful than a civil servant

Answer 1

Every Civil Servant e.g. an Ambassador, an Income Tax Officer or Policeman, is part of a wider 'Ministry' or an Arm of the government.
The Ministers are elected through a democratic vote and are popular representatives of the people, given the authority to make laws and govern.
Civil Servants are  not elected representatives and cannot make laws. They do not represent the people and are employed after giving tests and going through a training process.
They are answerable to people who are elected in Power and must work under them.

E.g. The Chief Minister of UP is elected by the people, while Police Constable is working under them. He might be responsible for his own team, but at the end the CM has more power

Answer 2

Ministers in the state, union territories and in the central government report to the Chief Minsters or the Prime Minister, who are all elected by the people of the country through elections. The Bureaucrats or the Civil Servants function under the respective ministers and are responsible for the smooth functioning of the government. Hence, Ministers are more powerful than the Bureaucrats in their functioning.