Need two separate search fields which index different categories…

add_filter('relevanssi_modify_wp_query', 'rlv_category_switch');
function rlv_category_switch($query) {
    if (!isset($_GET['cs'])) {
        $query->set('category__not_in', array(CAT_ID));
    }
    else {
        $query->set('category__in', array(CAT_ID));
    }
    return $query;
}

Add this to your theme functions.php and replace CAT_IN with the category ID of the category you want to exclude. Then in the single category search form, add this:

<input type="hidden" name="cs" value="1" />

That should do it.