Excluding specific categories from WP_Query
This is in the codex. You can exlclude specific categories from WP_Query. Where array(2, 6) are IDs for categories to be excluded in this example.
$query = new WP_Query( array( 'category__not_in' => array( 2, 6 ) ) );
See the codex:
NOTE: If you are trying to exclude category by the name of category
First you would do this to find the category ID by providing category name.
$category_id = get_cat_ID( 'My Category' );
then add the returned
$category_id in your WP Query arguments it would look like this:
$query = new WP_Query( array( 'category__not_in' => array( $category_id ) ) );