A client wanted to completely remove the area on the Cart page where cross-sells show. This is helpful if you have dozens of products with cross-sells and you don’t want to go and edit every single page.

Add the following snippet in your current theme’s function.php file:

// Remove cross-sells at cart
remove_action( 'woocommerce_cart_collaterals', 'woocommerce_cross_sell_display' );

Note: I strongly recommend you to do this edit on a child theme.