Strip a word from wp_list_categories

I assume you want to replace the “news” string in the category names and not in the category links.

The default category walker contains this line:

$cat_name = apply_filters( 'list_cats', $cat_name, $category );

that allows you to modify the category names that will be displayed.

So you could try (untested):

<ul class="subcats-blog">     
    <?php
        if ( is_category() ) {
            $current_cat = get_query_var('cat');

            // Add your custom replace filter:
            add_filter( 'list_cats', 'wpse_155534_replace' );

            wp_list_categories('&title_li=&child_of=".$current_cat);

            // Remove your custom replace filter:
            remove_filter( "list_cats', 'wpse_155534_replace' );
        }
    ?>
</ul>

where

/**
 * Replace the "news" string in the category names
 *
 * @see http://wordpress.stackexchange.com/a/155539/26350
 *
 * @param  string $cat_name
 * @return string $cat_name
 */
function wpse_155534_replace( $cat_name )
{
    return str_ireplace( 'news', '', $cat_name );
}