Hi
Message deletion is not synced across devices (and there is no way to enable this). Messages instead need to be deleted separately on each device (this is also how the app works across any additional Apple devices, such as a computer, iPad, etc).
The Mirror my iPhone setting for Apple Watch determines only how you are notified about new messages. If you choose Custom, for example, you can decide whether your watch shows alerts, whether sound and/or haptic alerts are provided and whether (including how many times) alerts are repeated when new messages are received.
To delete a Messages conversation on your watch:
- Open the Messages app on your watch:
- When viewing the time, go to the Home screen (by pressing once on the Digital Crown) > tap on the Messages app icon.
- Or use Siri (eg "hey Siri, open Messages").
- When viewing the conversation list, swipe left on the conversation that you wish to delete > tap Delete / Trash.