By default K2 Introtext limit will not work if you are using multiple categories in a Menu. To do this you need to change small code which is super easy...
Open 'category_item.php' and search for below code
<?php echo $this->item->introtext; ?>
Change/replace the above code with below code
<?php echo K2HelperUtilities::wordLimit($this->item->introtext, 15); ?>
15 is the word limit I gave, you can change the word limit to suit your need.