You can excise sites one by one, though it's a bit clunky. If you're logged in, click "Personalize" at the top-right, then type in the publication's name under

You can excise sites one by one, though it's a bit clunky. If you're logged in, click "Personalize" at the top-right, then type in the publication's name under "Adjust Sources", click + (if it's found) to add it to your customized sources list, then drag the frequency slider for that source all the way to the left. I'm not sure if this precisely blocks it, but it should mostly get it out of your Google News feed.