$cat_ids = wp_list_pluck( $cat, 'term_id' );
Once you get the category ids as you have mentioned above, you can search for the key having the category id 68 as
$key = array_search('68', $cat_ids);
Once you get the key, you can unset/remove that from the array as
unset($cat_ids[$key]);
Once that is removed, you can use the implode function the way you are currently using.
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