clearYoutubeWatchLaterList.js

// Go to https://www.youtube.com/playlist?list=WL&disable_polymer=true
// Open the javascript console (CTRL+SHIFT+K in Firefox)
// Run the following code:

function loadMore() {
  // Click the "Load More" button
  var el = document.getElementsByClassName('browse-items-load-more-button');
  if (el.length) {
    el[0].click();
    return true;
  }
  return false;
}

function sleep(ms) {
  // From https://stackoverflow.com/a/39914235/836995
  return new Promise(resolve => setTimeout(resolve, ms));
}

async function removeVideos() {
  while(true){
    var el = document.getElementsByClassName('pl-video-edit-remove'); // find the x
    if (el.length) {
      el[0].click(); // click the x to remove the video
      await sleep(1000); // sleep, so as not to overload the connection
    } else {
      if (!loadMore()) { // try to load more videos
        return; // stop if there is no load more button
      }
    }
  }
}

removeVideos();