How to truncate the description in the admin panel for a custom taxonomy

One approach is to use JavaScript to add the maxlength attribute to the term description field:

function wpse_term_description_attributes() { ?>
    <script type="text/javascript">
        jQuery(document).ready(function($) {            
            $( '.taxonomy-custom_taxonomy_name #description, .taxonomy-custom_taxonomy_name #tag-description' ).attr( 'maxlength', '20' );
        });
    </script><?php
}
add_action( 'admin_head', 'wpse_term_description_attributes' );

Replace custom_taxonomy_name with the name of your taxonomy, and customize the value assigned to the maxlength attribute as needed.