Welcome to the community, @Jessica_Farrell !
Deleting records is not currently supported with the built-in (point-and-click) automation actions. I think it would be really useful for Airtable to add this feature — you might want to suggest it to them by emailing support@airtable.com.
My guess is that you could possibly write a JavaScript for your automation that can delete a record for you. I am not yet proficient in JavaScript, so someone else would have to verify if that is indeed possible.
Alternatively, the way that I currently do this is that I use Integromat to automate the deletion of my records. Integromat is a no-code/low-code way of automating Airtable.
(Note that I am a professional Airtable consultant and a Registered Integromat Partner, and the Integromat link contains my personal referral code.)