This is one of the most annoying features on the current Youtube.com website: If you manage to open the miniplayer – always an accident for me – the miniplayer will stay active on the site, seemingly forever.
Even when you’ve watched every video on the playlist, it will stay open. You can remove all but one of the videos, but the final one cannot be removed, so the miniplayer stays on.
The solution is, however, simple. You can expand the miniplayer to the main youtube player and then the playlist, or queue, appears below the video. There you simply choose to clear the queue.
So, it is actually rather simple. But if you do an online search for this problem, you will find it many times but few seem to have found a solution.