How to remove an item from magento shopping cart automatically?

$cartHelper = Mage::helper('checkout/cart');
$items = $cartHelper->getCart()->getItems();
foreach ($items as $item) {
    if ($item->getProduct()->getId() == $productId) {
        $itemId = $item->getItemId();
        $cartHelper->getCart()->removeItem($itemId)->save();
        break;
    }
} 

Note:
The ItemId (ID of an item in the cart) is not the same as the ProductId of the product it represents. Try iterating through the items in the cart until you find the one with the ProductId you want to remove.