Add the following PHP code to your child theme functions.php file.

// hide coupon field on the cart page
function disable_coupon_field_on_cart( $enabled ) {
	if ( is_cart() ) {
		$enabled = false;
	}
	return $enabled;
}
add_filter( 'woocommerce_coupons_enabled', 'disable_coupon_field_on_cart' );