Contrary to all other answers, if you remove the entire accordion block, you will also remove the recent orders and wishlist accordion items, not just the cart ones.
You should overwrite the Mage_Adminhtml_Block_Customer_Edit_Tab_View_Accordion
and comment out or remove the following code:
// add shopping cart block of each website
foreach (Mage::registry('current_customer')->getSharedWebsiteIds() as $websiteId) {
$website = Mage::app()->getWebsite($websiteId);
// count cart items
$cartItemsCount = Mage::getModel('sales/quote')
->setWebsite($website)->loadByCustomer($customer)
->getItemsCollection(false)
->addFieldToFilter('parent_item_id', array('null' => true))
->getSize();
// prepare title for cart
$title = Mage::helper('customer')->__('Shopping Cart - %d item(s)', $cartItemsCount);
if (count($customer->getSharedWebsiteIds()) > 1) {
$title = Mage::helper('customer')->__('Shopping Cart of %1$s - %2$d item(s)', $website->getName(), $cartItemsCount);
}
// add cart ajax accordion
$this->addItem('shopingCart' . $websiteId, array(
'title' => $title,
'ajax' => true,
'content_url' => $this->getUrl('*/*/viewCart', array('_current' => true, 'website_id' => $websiteId)),
));
}
Copy app/code/core/Mage/Adminhtml/Block/Customer/Edit/Tab/View/Accordion.php
to app/code/local/Mage/Adminhtml/Block/Customer/Edit/Tab/View/Accordion.php
and do your edits.