There's an idea related to this that you can vote for: https://community.tableau.com/ideas/3951. Right now, I believe you have 2 options.
1. As described on the idea above, you could setup a user account on Tableau Server that works as a distribution list (i.e. assign a distribution list e-mail to that user).
2. Use tabcmd to send email messages as described on this article: Tabcmd Examples | Tableau Software. See section 'Use tabcmd to send email messages'.
Hope this helps!