Answer:
No, President can not remove Rodriguez as a Supreme Court Justice because the Constitution does not give him/her that power or authority.
Step-by-step explanation:
According to the Article II, Section II, Clause II of the US Constitution, a President enjoys the rights of appointing or nominating people for various offices, in which the Chief Justice of the Supreme Court is included.
Though the Constitution gives President right and power to nominate a Chief Justice, it does not give power to remove him from his office. Instead, according to the Article I, Section III, Clause VI of the Constitution, Chief Justice have right to preside over a President in case of impeachment.
The position of Chief Justice is considered to be the highest-ranking office in the federal judiciary of the US. Role of a Chief Justice is to operate as per the laws of the Constitution and not President. So, if Justice Rodriguez perceives President's policies to be against laws then he has right to vote against it.