Clark, 45, would be the first person executed in the state since 1960, when David Cooper Nelson, accused of killing a California man who picked him up hitchhiking, was put to death in the gas chamber.
He is scheduled to die by lethal injection for the 1986 murder of nine-year-old Dena Lyn Gore of Artesia, N.M.
"Since New Mexico's last execution 41 years ago, 109 countries have stopped using the death penalty," said Michele Williams, Amnesty International's deputy director for the Western United States. "Just last year, the state of Illinois declared a moratorium on all executions, and a growing movement of concerned Americans is becoming increasingly uncomfortable with the unfair and arbitrary application of state-sponsored killing. This is not the time for New Mexico to take such a large and deadly step backwards."
Clark has volunteered twice to be put to death and has twice changed his mind. In August, after a series of hearings, a court found Clark competent to drop his appeals.
Clark's attorneys charge that his mental impairment and severe conditions in the penitentiary make him incapable of making such a decision.
Johnson, R-N.M., has said he doesn't plan to interfere with Clark's execution.
He also told reporters that he would not be swayed by a request for leniency from an envoy from Pope John Paul the Second. The U.S. Ambassador for the pope, Archbishop Gabriel Montalyo, wrote Johnson, "In the name of the Holy Father, I beseech you to spare the life of Terry Clark."
Notable deaths of 2014 [PHOTOS]