Hello and welcome to Apple Support Communities, saveen23!
I understand you want to mute the notification sounds on your Apple Watch. I'd be happy to provide information to help you out.
Use the steps here to mute your notifications: Change the audio and notification settings on your Apple Watch
- Touch and hold the bottom of the watch face. Wait for Control Center to show, then swipe up.
- Tap
. This turns on Silent Mode. You can still receive haptic notifications.

To silence an alert or notification as it sounds, rest your palm on the display for at least three seconds or until you feel a tap. If it doesn't work, see if the Cover to Mute setting is on: On your iPhone, open the Apple Watch app, go to the My Watch tab, then tap Sounds & Haptics.
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Have a great day!