An automation will usually let contacts re-enter your workflow after they've finished it.
But if you need contacts to go all the way through just once (say, you're offering a one-time 20% off discount for people who subscribe via a specific form), this is quite simple to do:
1) Head over to the Engage menu. Under Automations, click View all.
2) Click the settings button of your automation and choose Options.
3) An options window will come up. Untick Funnel contacts more than once and save your changes.
Done! From now on, any contacts funneled into your automation won't be able to re-enter it.
Can I stop contacts from re-entering the automation only from a specific trigger onwards?
You bet! Simply edit the automation and then edit the trigger you want. Untick Funnel contacts more than once and save the trigger. Contacts won't re-enter it anymore.