OK, solved! It is just a confusion made by JCE Editor, because he gives you Read More button and functionality but actually it can't be done in core Joomla, because Joomla don't have Read More in Category description functionality.
So solution is not elegant, but serves. You can create separate articles and in Category description you can add Read More link to full separate article.
More "elegant" solution is requires hard-coding, so if anybody know how and what, pls. share!