Hey there, and welcome to Apple Support Communities, cherisa14!
From your post, it sounds like your emails are not being deleted on your Apple Watch after removing them from your iPhone or Mac. I use Mail often on my Apple Watch as well, so I’d be happy to help.
If you haven’t already, I’d recommend restarting your Apple Watch and iPhone before we begin troubleshooting and checking for any updates for your Apple Watch. Update your Apple Watch can help with those steps.
Next, do you see any alerts in My Watch > Mail > Accounts on your iPhone? If so, I’d recommend tapping on Accounts to clear the error, then try again.
If restarting the devices or clearing the error doesn’t resolve the behavior, try using the steps below to remove the Mail app from your Watch; be sure to restart your devices between removing and reinstalling the app:
"Apple Watch: To delete the app, open the Watch app on your iPhone and tap the My Watch tab. Scroll to the app you want to remove, then tap it. Turn off Show App on Apple Watch, and wait for it to disappear from your watch's Home screen. To reinstall the app, scroll down to Available Apps in the My Watch tab and tap Install."
If an app unexpectedly quits, stops responding, or won’t open
When you unpaired your iPhone and Apple Watch did you restore your Apple Watch from a backup or did you set it up as new when pairing again?
I hope that helps, and thanks for using Apple Support Communities. Have a great day!