Yes he can, but indirectly: in the federal workforce there are more contractors than actual government employees [1], and they share similar roles and responsibilities. Those contracts can be terminated at the pleasure at the government. Rip up the contracts, and you have essentially witheld funds for programs that no longer have adequate staffing.
Elon wasn't given that authority. If he asserted it early on it was later taken away. It's been said over and over that his access is read-only and any findings are to be made fully transparent to the public.
https://blog.simpletechnology.io/why-would-you-want-to-work-...
https://www.pogo.org/analysis/contractors-and-true-size-of-g...