Yes and no. The Vice President cannot be fired by the President, but the Vice President is free to step down from their position on his own accord.
Usually Vice Presidents will not resign voluntarily because they have a higher chance of obtaining Presidential powers in under three years than if they were thrown out.
Nevertheless some recent instances include George Bush Sr to Bush Jr as well as Reagan to Bush Sr for no particular reason other than personal reasons. But in light of these things it has been stated by multiple sources (including Wiki) that it is not recommended that any Vice Presidential inquires do themselves in when trouble arises with either Congress or a popular vote begins taking place because “you might never know what could happen”