Wordpress - Custom Taxonomy specific to a Custom Post type

First of all, if you want to show taxonomy metabox only to your custom post type, then register the taxonomy to only that custom post type by passing the custom post type name as argument in the register_taxonomy() function. By doing this, the taxonomy metabox appears only to custom post type. If you don't want to show category metabox to your custom post type, then remove the term category as an argument while registering your custom post type and instead include the taxonomy slug name like this: 'taxonomies' => array( 'post_tag', 'your_taxonomy_name'). Here is the code of how I achieved that.

I have registered a custom taxonomy with slug "themes_categories" under under custom post type themes:

function themes_taxonomy() {
    register_taxonomy(
        'themes_categories',  // The name of the taxonomy. Name should be in slug form (must not contain capital letters or spaces).
        'themes',             // post type name
        array(
            'hierarchical' => true,
            'label' => 'Themes store', // display name
            'query_var' => true,
            'rewrite' => array(
                'slug' => 'themes',    // This controls the base slug that will display before each term
                'with_front' => false  // Don't display the category base before
            )
        )
    );
}
add_action( 'init', 'themes_taxonomy');

Then to change the permalink, I have created the following function:

function filter_post_type_link( $link, $post ) {
    if ( $post->post_type !== 'themes' )
        return $link;

    if ( $cats = get_the_terms($post->ID, 'themes_categories') )
        $link = str_replace('%themes_categories%', array_pop($cats)->slug, $link);

    return $link;
}
add_filter('post_type_link', 'filter_post_type_link', 10, 2);

Then I registered a custom post type with slug "themes" as below:

// Registering Custom Post Type Themes
add_action( 'init', 'register_themepost', 20 );
function register_themepost() {
    $labels = array(
        'name' => _x( 'Themes', 'my_custom_post','custom' ),
        'singular_name' => _x( 'Theme', 'my_custom_post', 'custom' ),
        'add_new' => _x( 'Add New', 'my_custom_post', 'custom' ),
        'add_new_item' => _x( 'Add New ThemePost', 'my_custom_post', 'custom' ),
        'edit_item' => _x( 'Edit ThemePost', 'my_custom_post', 'custom' ),
        'new_item' => _x( 'New ThemePost', 'my_custom_post', 'custom' ),
        'view_item' => _x( 'View ThemePost', 'my_custom_post', 'custom' ),
        'search_items' => _x( 'Search ThemePosts', 'my_custom_post', 'custom' ),
        'not_found' => _x( 'No ThemePosts found', 'my_custom_post', 'custom' ),
        'not_found_in_trash' => _x( 'No ThemePosts found in Trash', 'my_custom_post', 'custom' ),
        'parent_item_colon' => _x( 'Parent ThemePost:', 'my_custom_post', 'custom' ),
        'menu_name' => _x( 'Themes Posts', 'my_custom_post', 'custom' ),
    );

    $args = array(
        'labels' => $labels,
        'hierarchical' => false,
        'description' => 'Custom Theme Posts',
        'supports' => array( 'title', 'editor', 'excerpt', 'author', 'thumbnail', 'comments', 'revisions', 'post-formats', 'custom-fields' ),
        'taxonomies' => array( 'post_tag','themes_categories'),
        'show_ui' => true,
        'show_in_menu' => true,
        'menu_position' => 5,
        'menu_icon' => get_stylesheet_directory_uri() . '/functions/panel/images/catchinternet-small.png',
        'show_in_nav_menus' => true,
        'publicly_queryable' => true,
        'exclude_from_search' => false,
        'query_var' => true,
        'can_export' => true,
        'rewrite' => array( 'slug' => 'themes/%themes_categories%', 'with_front' => FALSE ),
        'public' => true,
        'has_archive' => 'themes',
        'capability_type' => 'post'
    );
    register_post_type( 'themes', $args ); // max 20 character cannot contain capital letters and spaces
}

There are few things you have to remember while registering custom post. Change the "has_archive" parameter to the custom post type slug name and the rewrite slug name as 'slug' => 'custom_post_type_slug/%taxonomy_slug%.

Now when you add a new post type in the right post type page, you will see the permalink as http://www.example.com/wordpress/themes/%themes_categories%/post-name/. If the custom taxonomy for this post is not selected, the permalink will remain http://www.example.com/wordpress/themes/%themes_categories%/post-name/, which will then show a bad request.

To correct this, we create a default term in the custom taxonomy (same as uncategorized in categories).

Add this to functions.php:

function default_taxonomy_term( $post_id, $post ) {
    if ( 'publish' === $post->post_status ) {
        $defaults = array(
            'themes_categories' => array('other'),
        );
        $taxonomies = get_object_taxonomies( $post->post_type );
        foreach ( (array) $taxonomies as $taxonomy ) {
            $terms = wp_get_post_terms( $post_id, $taxonomy );
            if ( empty($terms) && array_key_exists( $taxonomy, $defaults ) ) {
                wp_set_object_terms( $post_id, $defaults[$taxonomy], $taxonomy );
            }
        }
    }
}
add_action( 'save_post', 'default_taxonomy_term', 100, 2 );

Now when the custom taxonomy is left blank. the permalink becomes http://www.example.com/wordpress/themes/other/post-name/ automatically.

Lastly, don't forget to flush the rewrite by clicking on the "Save Changes" button in the permalink setting of the WP backend admin section, otherwise you will be redirected to 404 error. I hope this helps you.