By default, K2 search result show full content. So, instead of full content if you want to limit the text with Read More button, follow below few steps.

1. Open generic.php file (components\com_k2\templates)
2. Go to Line 86
3. Change below code

   <?php echo $item->introtext; ?>
   

4. To this

   <?php echo K2HelperUtilities::wordLimit($item->introtext, 120); ?>
   

5. That 120 is number of words you desire to have.

NOTE: Remember to use overrides