Exclude category from get_the_category

$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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