Use this code

**Your Controller Action**

public function deleteAction()
        {
            if((int) $this->getRequest()->getParam('isAjax') == 1){
                $id = (int) $this->getRequest()->getParam('id');
                if ($id) {
                    try {
                        $this->_getCart()->removeItem($id)->save(); 
                        $message = $this->__('Item was removed from your shopping cart.');
                        $response['status'] = 'SUCCESS';
                        $response['message'] = $message;
                        $this->getResponse()->setBody(Mage::helper('core')->jsonEncode($response));
                        return;

                    } catch (Exception $e) {
                $response['status'] = 'ERROR';
                $response['message'] = $this->__('Cannot remove the item from shopping cart.');
                Mage::logException($e);
                    }
                }
            } else {
                return parent::deleteAction();
            }
        }

**Js Function**

<script type="text/javascript">
            var deleting = 0;
            productRemoveFromCart = function(url, elem){
                deleting = deleting + 1;
                jQuery(elem).parent().parent().animate({ opacity: 0.5 }, 200, function() { });
                if (!url) {
                        //alert('Problem');
                }
                url = url.replace("checkout/cart","ajax/index");
                if(window.location.protocol == "https:") {
                    url = url.replace("http:","https:");
                }
                url += '&isAjax=1';
                var data = 'isAjax=1';
                try {
                        jQuery.ajax( {
                                url : url,
                                dataType : 'json',
                                type : 'post',
                                data : data,
                                success : function(data) {
                                        deleting = deleting - 1;
                                        if(deleting<1){
                                            var pagepath = window.location.pathname;
                                            if((pagepath.indexOf("onestepcheckout")>0)||(pagepath.indexOf("checkout/cart")>0)){
                                                location.reload();
                                            }
                                        }
                                },
                                error: function (data) {
                                    deleting = deleting - 1;
                                }
                                }); 
                } catch (e) {
                }
            }     
    </script>

**Button code**

<td class="a-center"><a href="javascript:void(0)" onclick="productRemoveFromCart('<?php echo $this->getDeleteUrl(); ?>',this);" title="<?php echo $this->__('Remove item')?>" class="btn-remove btn-remove2"><?php echo $this->__('Remove item')?></a></td>