how can I use WP_Query to exclude a specific tag.?

Use tag__not_in parameter. You have to use tag ID for this parameter

$args = array(
    'category_name' => $cat_name,
    'tag' => $tag_name,
    'post__not_in' => $sticky,
    'tag__not_in' => array($tag_id_1, $tag_id_2)
);

$my_query = new WP_Query( $args );

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