Start by tapping your profile icon, then Settings. Select Notifications and uncheck or toggle off the options for Stories from friends and any other story alerts you want to mute.
Go to your profile, then Settings, select Notifications, and simply uncheck the Stories from friends box! Once you do this, the next time your friend uploads a story, you won't get a notification.
Uncheck 'Stories from Friends' to remove broadcast pushes.
Read and understand that for ios/android - disable it for device only. Steps as follows:
Open OS System Settings > Apps > Snapchat > Notification Categories > and uncheck 'stories' - don't change the settings directly to the Snap or the chat delivery.
To turn off all story alerts:
1. Open Snapchat
2. Tap on your profile icon, then the Settings gear.
3. Select Notifications.
4. Click 3 dots to clear 'Stories from Friends' and 'Suggested Stories'.
This blocks the bulk story alerts in your account.