iOS 10 has added the ability to clear all notifications at once. Unfortunately this feature is only available for iPhone that is capable of 3D Touch.
Swipe down from top of screen to bring up the Notification Center screen. Use 3D Touch to press on the “x” icon on left top corner of a notification. You will be presented with an pop up option to “Clear All Notifications”. Tap on it to see all your notifications removed from the screen.