How do you bulk remove a category from posts?

You can make use of wp_remove_object_terms() to remove the desired category from a post.

What we will do is, run a custom query to get all the post with the associated category, and then loop through the posts and use wp_remove_object_terms() to remove the category

FEW NOTES:

• The code is untested and might be buggy. Be sure to test this locally first

• If you have a huge amount of posts, this might lead to a fatal error due to timing out. To avoid this, run the function a couple of times with a smaller amount of posts till the whole operation is complete

THE CODE:

add_action( 'init', function()
{
    // Get all the posts which is assigned to the uncategorized category
    $args = [
        'posts_per_page' => -1, // Adjust as needed
        'cat'            => 1, // Category ID for uncategorized category
        'fields'         => 'ids', // Only get post ID's for performance
        // Add any additional args here, see WP_Query
    ];
    $q = get_posts( $args );

    // Make sure we have posts
    if ( !$q )
        return;

    // We have posts, lets loop through them and remove the category
    foreach ( $q as $id )
        wp_remove_object_terms(
            $id, // Post ID
            1, // Term ID to remove
            'category' // The taxonomy the term belongs to
        );
}, PHP_INT_MAX );

You can just simply drop this into your functions file and then load any page back end or front end. You can then remove the code from your functions file