Email deletions should be synced across your devices. It may help to check that your devices are connected via Bluetooth. For the best performance from your iPhone and Apple Watch, including the most power-efficient communication between them, Apple recommends keeping both Bluetooth and Wi-Fi permanently enabled on your iPhone:
About Bluetooth and Wi-Fi on Apple Watch - Apple Support
To select your preferred notification alert methods for Mail on your Apple Watch:
On your iPhone, in the Watch app, go to: My Watch > Mail:
- Perhaps choose Custom and check, under Alerts, that Show Alerts is enabled.
- Tap on your email account (eg iCloud) > check that Show Alerts from iCloud (for example) is enabled > select Sound and/or Haptic, as desired.
Keep in mind that how notifications behave depends on the status of your devices and your settings. With Wrist Detection enabled, in order to bring notifications to your attention as soon as possible:
- If your iPhone is unlocked, then you will receive notification alerts on your iPhone instead of on your Apple Watch.
- If your iPhone is locked or asleep and your Apple Watch is unlocked (regardless of whether the watch display is asleep or awake) and on your wrist, you will receive notification alerts on your watch.
- If your Apple Watch is locked or has Do Not Disturb enabled, then notifications will go to your iPhone.
- More information: Notifications on your Apple Watch - Apple Support