Mandating Responsibility Act This bill establishes a private cause of action for employees who are harmed by their employer's COVID-19 vaccine mandate. An employee may bring an action against the employer for wrongful termination or other adverse employment actions for violating the mandate. An employee may also bring an action against the employer for wrongful death or serious injury related to the COVID-19 vaccine administration, if the employee received the vaccine solely to comply with the employer's mandate. An employee may recover damages (actual, compensatory, and punitive), injunctive relief, attorney's fees and costs, and other appropriate relief.