Go to K2, then click the "settings" button at the top right.
On the "administrator" tab, set the first option on the list "Use one editor window for introtext & fulltext" to "No".
Now, whenever you edit a K2 item, you will have two editor windows, one for introtext, one for full text.
Now you need to configure your item display options in your new category (and make sure it's not inheriting settings from another category) to either show or hide the intro text, whatever your preferences are.
Then make sure to only input text on the "full text" field.
An advanced tip is to show introtext in the item, put whatever most important first paragraph or highlight text or summary in the introtext, and format it differently (maybe a bigger font size, an outline, or whatever you want).