Magento 1.9 – Removing Products from Cart and Checkout

I have a helper that in the click of the button, according to the id of the product it adds the same to the stand.

But I need to do the reverse, a function that removed a product from the cart according to its product id on button click.

I search a lot about it, but I still did not find anything that could help me do the function to remove the product from the cart.

Edit: I tried this function below, but it removes all the products that are in the cart, not just the product according to its id.

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

Note: The above code is in a controller.

Ajax request code:

function removeCartaotoCart(){
                $j.ajax({
                    type:"POST",
                    url:"<?php echo Mage::getUrl('fol_carousel/ajax/removeCartao') ?>",
                    data:{

                    },
                    cache: false,
                    beforeSend: function(){
                        alert("beforeSend");
                    },
                    success: function(){
                        alert("Sucess removeCartao");
                    },
                    complete: function () {
                        alert("complete removeCartaotoCart");
                    },
                    error: function (x,y,z) {
                    alert("error");
                    alert(x);
                    alert(y);
                    alert(z);
                    window.location.reload();
                    history.go(0);
                    window.location.href=window.location.href;
                  }
                });
            }

Edit 2:

Button code:

<button type="button" title="<?php echo Mage::helper('core')->quoteEscape($this->__('Add to Cart')) ?>" class="button btn-cart" onclick="addCartao('<?php echo $_product->getId(); ?>')" name="cartaoMensagem<?php echo $_product->getId(); ?>"><span><span><?php echo $this->__('Add to Cart') ?></span></span></button>

Ajax request that adds the product to the cart and change the button text / Address the second request of which the code is above (this request is not so important in this question, but for information, I also put it):

function addCartao(product_id){
                $j.ajax({
                  type: "POST",
                  url: "<?php echo Mage::getUrl('fol_carousel/ajax/addCartao') ?>",
                  data: {
                    product_id: product_id
                  },
                  dataType: 'json',
                  cache : false,
                  beforeSend: function () {

                  },
                  success: function (retorno) {
                    var button = $j('button[name=cartaoMensagem' + product_id + ']');

                  if($j(button).text() == 'Comprar'){
                    $j('#cartao').find(':button').not(button).attr('disabled',true);
                    $j(button).html('<span>Remover</span>');
                    $j('.item-custom').append('<tr id="trAppend"><td class="a-center lc-thumbnails"><img src="' + retorno['imagem'] + '" width="50" height="50" alt="' + retorno['name'] + '"></td><td><h3 class="product-name">' + retorno['name'] + '</h3></td><td class="a-center">1</td><td class="a-right"><span class="cart-price"><span class="price"> R$ ' + retorno['price'] + '</span></span></td></tr>');
                    getSubTotal();
                    getGrandTotal();
                  } else{
                    $j('#cartao').find(':button').attr('disabled',false);
                    $j(button).html('<span>Comprar</span>');
                    $j('.item-custom #trAppend').remove();
                    removeCartaotoCart();
                    getSubTotal();
                    getGrandTotal();
                  }

                  },
                  complete: function () {

                  },
                  error: function (x,y,z) {
                    alert("error");
                    alert(x);
                    alert(y);
                    alert(z);
                    window.location.reload();
                    history.go(0);
                    window.location.href=window.location.href;
                  }
              });
            }