Ok, I revisited this and revised my answer.. 

But like I said before:

> the hook you are (trying) to use won't/can't work for the purpose you are aiming for, simply because its only occurrence is in `class-wp-posts-list-table.php`, which nomen est omen is used to show the post list, the right place should be `class-wp-terms-list-table.php`. 

<br>
1. What you can do is the following:

 - Making use of the [`admin_head-$hook_suffix`](http://hookr.io/3.9.1/actions/do_action/admin_head_hook_suffix/) and [`get_terms`](http://hookr.io/3.9.1/filters/apply_filters/get_terms/) hook


		add_action(
			'admin_head-edit-tags.php',
			'wpse152619_edit_tags_trim_description'
		);
		function wpse152619_edit_tags_trim_description() {
			add_filter(
				'get_terms',
				'wpse152619_trim_description_callback',
				100,
				2
			);
		}

		function wpse152619_trim_description_callback( $terms, $taxonomies ) {
			// print_r($taxonomies);
			if( 'category' == $taxonomies[ 0 ] ) {
				foreach( $terms as $key => $term ) {
					$terms[ $key ]->description =
						wp_trim_words(
							$term->description,
							12,
							' [...]'
						);
				}
			}
			return $terms;
		}
    
    This trims the description to a specified word count.

<br>
2. Another often found possibility is removing the default column and create a new one:
 
 - Making use of the [`manage_{$this->screen->taxonomy}_custom_column`](http://hookr.io/3.9.1/filters/apply_filters/manage_screen_taxonomy_custom_column/) and [`manage_{$this->screen->id}_columns`](http://hookr.io/3.9.1/filters/apply_filters/manage_id_columns/) hook

		function wpse152619_create_new_description_column( $columns ) {
			if ( $_GET[ 'taxonomy' ] == 'category' ) {
				// uncomment next line to remove default description column
				//unset( $columns[ 'description' ] );
				// create new description column
				$columns[ 'new_description' ] = 'New Description';
				return $columns;
			}
			return $columns;
		}
		add_filter(
			'manage_edit-category_columns',
			'wpse152619_create_new_description_column'
		);


		function wpse152619_new_description_column_content(
			$deprecated,
			$column_name,
			$term_id
		) {
			if ( $column_name == 'new_description' ) {
				$new_description =
					wp_trim_words(
						term_description(
							$term_id,
							$_GET[ 'taxonomy' ]
						),
						12,
						' [...]'
					);
				echo $new_description;
			}
		}
		add_filter(
			'manage_category_custom_column',
			'wpse152619_new_description_column_content',
			10,
			3
		);

<br>
3. Also possible would be:

 - Extend the class [`WP_List_Table`](http://codex.wordpress.org/Class_Reference/WP_List_Table) yourself, like `WP_Terms_List_Table` it does;
 - In your case the main goal would be redefining the `column_description` method;
 - Additionally, create a new template, similar to `edit-tags.php`, but using your newly create class;
 - Then you would have to make sure that your new template is loaded instead of the default one;
 - Ok, but that's just a outline of would be possible too. Makes no sense in this simple case, but for advanced use cases this would be an approach to consider.

<br>

I'm sure the above should solve your problem. Note that I did the examples for category edit page, but how to do this for custom taxonomies should be apparent. Depending on what is needed a simple or elaborate approach can be chosen. In you case the first one should be just fine.


Last but not least the following function is handy to get the information you need:

	add_action( 'admin_head', 'wpse152619_dbg_dev' );
	function wpse152619_dbg_dev() {
		global $pagenow;
		print_r( $pagenow );
		echo '<br>';
		print_r( $_GET[ 'taxonomy' ] );
		echo '<br>';
		$current_screen = get_current_screen();
		print_r( $current_screen->id );
	}