This is known as an expandable post summary. The only way to do this with a blogger blog is to modify your blog template. There is a an official article from blogger that explains the exact steps needed to set this up. Before you try this, though, I'd like to clarify a few points.
- Before you make any changes to your template you should download a backup copy first. The blogger article doesn't mention that until the end of the article....after you've made all your changes.
- Make the changes to a local copy of your backup template from step 1. Edit the file using WordPad, it is MUCH easier than using the web editor. When the changes are complete, upload your template.
- The article references 'Classic templates' and 'Layout'. If you can drag page elements around in the layout editor, use the Layout code. Chances are if you've started your blog in the past year you are not using the classic templates.
- Remember that once you finish the edits to the template, you must modify each post to indicate where the cutoff should be. You won't see any difference in any of your previous posts, so you will have to go back and edit all posts that you want to add this feature to.
Don't be intimidated by the XML. As long as you have a backup copy of your template, you can experiment all you want until you get things working.
If you are interested in learning more about your blogger blog, I recommend the book "Google Blogger". It's a great resource to guide you through everything you need to know about blogger blogs.