You can use filters in gmail…
1. click on the “Settings” link at the top right of the main gmail page
2. click on the “Filters” tab
3. click on the “Create a new filter” link
4. enter criteria in the pertinent fields that uniquely describe the email you want auto-deleted.
5. click the “Test Search” button to ensure it actually grabs the email you want… and only those emails. You don’t want any false positives getting trashed.
6. after successful test, click the “Next Step” button
7. choose the action you want applied.
Since this is your first use of the filter functionality, I suggest not selecting the “Delete it” option. Instead, try applying a label and/or archiving it instead. Try it that way for a few days to ensure that you’re really not getting any false positives.
Then later, once you’re certain the filter is golden, go back and edit the filter action to “Delete it” instead.