Thanks for reaching out.
From Appearance > Theme Settings > Blog you can set the Archive Post Content to either Full Post Content or Post Excerpt. If you set it to Full Post Content you can use the read more quicktag to split your posts with a Continue reading button. If you use the Post Excerpt option an auto excerpt will be applied if a manual excerpt isn’t set.
If you’re not sure how to use the more quicktag, please, see the WordPress documentation page here: https://en.support.wordpress.com/more-tag/.
It’s, unfortunately, at this stage, not possible to change the blog archive layout for mobile vs desktop.
Hope this helps a little to explain the options Puro can offer.