To remove elected officials before their term expires is called?

Answer 1

Impeachment is not the only answer. A "recall" election may be.

In some states, state legislators and other state or local elected officials may be removed from office before the expiration of their established terms not only by action of the legislature itself through an "Expulsion" (for executive officers through an "impeachment" and conviction by the legislature), but also by the voters through a "recall" election procedure. While an expulsion is an internal authority of legislative bodies incident to their general powers over their own proceedings and members, recall is a special process outside of the legislature itself, exercised by the people through a special election.

What this means is that Senators or Representatives of Congress, as written in the Constitution, are able to use a process called "expulsion" to expel one of their members, usually requiring a 2/3 vote of the rest of the members. There is no provision in the Constitution for their constituents to remove them. The "recall" process is outside of the Constitution, and is the means by which the people can remove a member from Congress. The process requires a petition which has signatures of at least 25% of the vote which the elected official had received. After this is obtained, a special election can be set up to select a different person for the office of the person to be removed.

Answer 2

Recall.