The first option for removing the “Badger 14” senators is for the Assembly to impeach them by a majority vote and, if impeached, for the Senate to convict them by a two-thirds vote. The provisions for impeachment and removal upon conviction are set out in Art. VII, Section 1, of the Wisconsin Constitution (available online here) which reads:
Impeachment; trial. The court for the trial of impeachments shall be composed of the senate. The assembly shall have the power of impeaching all civil officers of this state for corrupt conduct in office, or for crimes and misdemeanors; but a majority of all the members elected shall concur in an impeachment. On the trial of an impeachment against the governor, the lieutenant governor shall not act as a member of the court. No judicial officer shall exercise his office, after he shall have been impeached, until his acquittal. Before the trial of an impeachment the members of the court shall take an oath or affirmation truly and impartially to try the impeachment according to evidence; and no person shall be convicted without the concurrence of two-thirds of the members present. Judgment in cases of impeachment shall not extend further than to removal from office, or removal from office and disqualification to hold any office of honor, profit or trust under the state; but the party impeached shall be liable to indictment, trial and punishment according to law.
Although ultimately a matter for each member of the Assembly and Senate voting on impeachment and conviction, it would seem that the actions of the “Badger 14” to derail, indeed corrupt, the legislative process in violation of both their constitutional oath and specific provisions of law requiring their attendance meet the standard required for impeachment and conviction and removal from office.