deleted emails keep returning

Safe Boot, (holding Shift key down at startup), does the problem occur in Safe Mode? Could take 10 minutes.

Safe mode attempts to repair Disks & clears lots of caches & loads safe Drivers, & prevents loading of 3rd party extensions, so if Safe Mode works try again in regular boot.

To find out if it's system wide or user specific, try this...

Open System Preferences>Users & Groups, unlock the lock, click on the little plus icon, make a new admin account, log out & into the new account.

Does it work in the new account?

Mail>Preferences>Accounts>Your Account>Mailbox Behaviors, what path is Trash Mailbox set to?