Exclude posts from featuring

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:
https://codex.wordpress.org/Class_Reference/WP_Query#Category_Parameters

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 ) ) );