No, he cannot.

It seems President Trump is doing a good job of it getting rid of who he doesn’t wants..

SNIP
“President Donald Trump took over the White House less than a month ago, and in keeping with his reality television show catchphrase from The Apprentice - "You're Fired" - he has already removed more than 200 employees.
Some amount of turnover is typical for a new administration, but Trump has made massive changes during his first weeks in office. He offered buyouts to millions of government workers and put a stop to diversity, equity and inclusion (DEI) programmes.
On Friday, Trump fired the nation's top record keeper, US Archivist Colleen Shogan.
Later that night, he pledged to fire board of trustees members for the John F. Kennedy Center for the Performing Arts - and to name himself as chairman.
Here's a look at some of the major dismissals during Trump's first few weeks in office.”

BBC: 'You're fired': The people Trump has sacked since taking office

Snip
“Firings, freezes and layoffs: A look at Trump’s moves against federal employees and programs
Trump has also targeted specific government officials, firing Democratic Federal Elections Committee (FEC) chair Ellen Weintraub, according to a letter she shared online. Weintraub alleges her firing was not legal.

The FEC enforces campaign finance laws and oversees federal elections.

The president also dismissed Gwynne Wilcox, the first black woman to serve on the National Labor Relations Board, who is now suing the administration.”

yahoo.com - Youre fired people trump sacked