It's the President's job to determine how many employees are needed to do as Congress directs. That implies he also has the job of determining how many are not needed.
That is true. And when the president submits his/her budget to Congress, he/she can specify the staffing level they would like to have in each department.
Here is where it gets tricky, though. If the president requests a lower staffing level than currently exists and Congress appropriates budget for that staffing level, then the president can eliminate (lay off) the positions that were not funded. But if Congress ignores the president's budget request and funds all existing positions, it is almost impossible for the president to lay off or fire anyone to get down to the level he/she thinks is needed. The only option then is attrition - not replacing those who retire or quit.