Open the Settings app on your Apple Watch
Tap Sounds & Haptics
Turn off or adjust:
Silent Mode
Ringer and Alerts
Haptic Alerts
Cover to Mute
Enable Theater Mode
Swipe up to open Control Center
Tap the Theater Masks icon
Use Do Not Disturb
Swipe up to open Control Center
Tap the Do Not Disturb icon
Mute notifications for specific apps
Open the Watch app on your iPhone
Tap Notifications
Select the app
Toggle off Allow Notifications (or adjust the settings)
Silence the watch temporarily (Mute)
Press the Digital Crown to go to the Home screen
Open the Settings app
Tap Sounds & Haptics
Set Ringer and Alerts to off or lowest available level