Could you clarify that a bit? Perhaps just describe what you're trying to do rather than ask highly generalized questions.

Can I put a perl script to sleep and awake it whenever I want.
Yes, if, for example, the script has a signal handler.

I SSH to Linux server.
How does this relate to your question?

Do I need to run my perl script directly on server in order to sleep and awake?
Where it runs has no effect on its ability to sleep and be awakened. Perhaps what you are attempting will require the script to be on the server but we can't tell from the question.

Do tell.