you click the sign off button

The past tense of "sign off" is "signed off."

In employment: To start work, to end work.
In unemployment (UK): To sign on to benefits, to sign off benefits.
In computing: Log in and Log off

No, "sign off" is not hyphenated when used as a verb. However, it can be hyphenated when used as a noun (e.g., "She gave her sign-off on the project").

Most people sign off on their letters with the terms "love" or "sincerely". It is important to put the correct sign off, depending on who is being written to.