Secretary of State Rex Tillerson Aug. 28 unveiled his plan to eliminate several special envoys, including for climate change and the Iran nuclear deal, in a sweeping proposal to put his stamp on the agency and meet President Donald Trump’s demands for deep budget cuts.

In a letter to Republican Sen. Bob Corker of Tennessee, chairman of the Senate Foreign Relations Committee, Tillerson detailed how the job of many envoys will be subsumed into other agencies, such as the special representative for Afghanistan and Pakistan. Each elimination is accompanied by the amount of money the change will save.

The moves...