taxonomy-product_cat.php not working

Is your taxonomy-product_cat.php not working? All you may need is to add your WooCommerce theme support to your theme function’s file.

Add theme support for WooCommerce taxonomy templates

To allow your taxonomy-product_cat.php to register, you must add the WooCommerce theme support to your WordPress theme’s functions.php file.

add_theme_support( 'woocommerce' );

Refresh your permalinks

You could try to refresh your permalinks after you’ve created the file in your WordPress theme’s root directory.

You can do this by visiting your WordPress Dashboard>Settings>Permalinks and clicking Save Changes without changing anything.