How can I disable mail for a specific siteworx account?

Hello!
I;m dealing with a client that has an outdated WordPress installation along with some outdated plugins. As a result spammers are using her site to send thousands of spam emails per minute, so I'm trying to find a way to disable all mail activity for that specific account until she upgrades her website.

I know that I can just disable the site but if I do that she wont be able to log in and update her installation.

Thanks!