OK – so the best way to go is to filter out the posts with a PHP snippet like so:
add_action('pre_get_posts', 'exclude_category_posts');
function exclude_category_posts( $query ) {
if($query->is_main_query() && !is_admin()) {
$query->set('cat', array( -22, -33 ));
}
}
In the array: array( -22, -33 )
you need to update those values to match the ID of the category term(s) you want to exluded. Note it has to be a -negative value. So if the post ID was 37
then you would use -37