How to change core search result snippet?
You could build your own search result .tpl file inside your theme and take control over what displayed and the markup by creating a file named like search-results--[searchType].tpl.php After that you have to clear the cache in order to be recognized in theme registry 

In your case you could limit the number of words displayed or divide based on empty line which mean a pragraph.

Take a look at D7 theme suggestions