You said Powershell in the tags so I assume Windows.
If you have a handle to a process then you can do things to that process. The list of things you can do is documented in MSDN. In this case you would need to get handles to the individual threads in a process so you can suspend the threads: https://learn.microsoft.com/en-us/windows/win32/procthread/suspending-thread-execution
Doing this in POSIX is a bit easier. You just need to send a SIGSTOP signal to the target process. Then it and all its threads will stop running until you send SIGCONT.