This article explains how to clear the YouTube queue on a Chromecast using your Android device.
How to restore the Add to Queue buttons
The YouTube app on both Chromecast and Android devices allows one or more users to connect to the same TV and create a unique queue. With just a few taps on an Android device, you can clear the queue.
While a YouTube video is playing on the Chromecast, any Android device connected to the session will see the TV queue bar at the bottom of the screen.
Tap the X at the far right of the TV queue bar to clear the entire list of selected videos.