Open Snapchat
Tap your profile icon
Tap the gear icon to open Settings
Tap Notifications
Turn off the notification types you do not want
To stop all Snapchat notifications, disable Snapchat notifications in your device settings
On iPhone, go to Settings, tap Notifications, tap Snapchat, then turn off Allow Notifications
On Android, go to Settings, tap Apps, tap Snapchat, tap Notifications, then turn off notifications