Can the vice president of the United States be fired?
Does the vice-president serve at the discretion of the president, such that he or she can be removed from office at the president's will?
Are you only interested in whether the president can unilaterally remove the vice president from office or are you wondering if there other options, such as through an act of congress?
Only implied with the word 'fired', but as elaborated in the body of the question, I was looking for the former.
No. The President can not fire the Vice President.
Unlike the cabinet (e.g., Secretary of State, Attorney General, Secretary of Defense, etc.), and the White House Staff (e.g., Chief-of-Staff, Press Secretary, etc.) the office of the Vice President, his term and the requirements for his removal from office are all established explicitly in Article II of the Constitution.Office, Term—United States Constitution, Article II, Section 1
Removal—United States Constitution, Article II, Section 4
The executive Power shall be vested in a President of the United States of America. He shall hold his Office during the Term of four Years, and, together with the Vice President, chosen for the same Term, be elected, as follows [emphasis added]
The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.
Note that because the President and the Vice President are chosen for a term, the President has the option to choose a different Vice President for a re-election term. This happened with Andrew Jackson, who didn't get along with John C. Calhoun in his first term and chose Martin Van Buren as his running mate for his second term.