Last spring, CNN announced a text-only version of its site, linking to text-only articles, so people with spotty internet connections (such as the people then in Hurricane Irma's path) could access the news. Lite.cnn.io is ugly, but it's fast and functional. And it isn't the only pared-down news site.
CNN Lite lists 69 headlines (nice) that link to text-only versions. Unfortunately none of these articles link to their full versions, even if the text references illustrations or video. But if you're just looking for the bare news, or you're struggling to get a signal, the text site is an alternative to the blaring main site full of autoplay videos.
If you prefer a more subdued tone, NPR hosts its own text-only version at text.npr.org, which links to 10 top stories, with more headlines under News, Arts & Life, and Music. (As on CNN, you can't get to the full stories from the text version.)
Reuters runs a relatively light mobile front page with headlines and thumbnail images, but each headline leads to a more cluttered article page.
For the rest of your minimalist news reading, try news aggregators: Theoldgnews.com skins Google News in its older, simpler style; Pxlet collects tech headlines from several sources in a spare menu; and the news aggregation sites Techmeme, Mediagazer, Memeorandum and WeSmirch all have minimalist mobile versions of their already plain sites.
Of course, once you click through to the source site, those aggregators can't save you.