Excluded Custom Taxonomy Term Posts Displaying in loop

Try below methods:

1. Try by adding term ID in array like this 'exclude'=> '60' in array

2. If this is not working you can try with below WP_Query loop:

 $args = array(
        'post_type' => 'careers',
        'tax_query' => array(
            'relation' => 'AND',
            array(
                'taxonomy' => 'careers_categories',
                'field'    => 'term_id',
                'terms'    => array( 60),
                'operator' => 'NOT IN',
            ),
        ),
    );
    $query = new WP_Query( $args );