If you have a video on your channel that you want to completely delete, you can do this by going to Menu -> Your channel name;
Then select 'Videos';
Click on the video you want to delete and choose 'Settings';
At the right of the screen you will see 'Video State', and 'Delete Video';
After you've click on 'Delete Video' you will see a pop-up, click on this to fully delete your video;