With Easy Digital Downloads, a cart icon, item quantity, and cart total is shown in Themedd’s secondary menu. This can be completely disabled via the customizer, or by using the themedd_edd_show_cart filter hook.

/**
 * Disable the EDD cart.
 *
 * @return boolean Whether or not the EDD cart should be shown.
 */
function themedd_snippet_disable_edd_cart() {
	return false;
}
add_filter( 'themedd_edd_show_cart', 'themedd_snippet_disable_edd_cart' );

PHP should be added to your child theme's functions.php file.