The topic of duplicate content has changed over the years. Here is one older question: What is duplicate content and how can I avoid being penalized for it on my site?. I have written some examples of how Google determines duplicate content, however, I could not find it quickly. Trust me, it would quickly put you at ease. The up-shot is this. Google knows what is duplicate content and what is not.
Your situation, as you describe it, is perfectly normal. The technique of using content snippets is commonly used in blogs to tease a story on the home page or category and tag pages. Google and indeed Bing expect this. Indeed, they fully understand the "Read More" button/link.
What you want to make sure you do are 3 things.
Your original post should have a canonical tag that points to itself.
From the Google page on the topic, https://support.google.com/webmasters/answer/139066?hl=en
<link rel="canonical" href="https://example.com/dresses/green-dresses" />
You could use the code example in the
<head> section of your HTML and change the URL to point to the page itself.
This tells Google this is the original copy of the content.
When you create your content snippet, do not make it too large. Google will understand that this is a content snippet. I cannot recommend a size limit, however, you want it big enough to tease the story and short enough to be a snippet.
Advice: I like avoid cut and paste here. I prefer to write a teaser from scratch.
You can certainly use "Read More" for a button or a link. Make sure it immediately follows the content snippet.
Advice: I avoid "Read More" links and buttons. The reason is simple. Do you really want to rank for the terms "read more"? I don't. Instead, I use either the title of the page you are linking to or a teaser. For example, "Learn more about how eating almonds is good for men's health." is not only a good teaser but could also be the title of the page you link to.