Updating site content after an AJAX call without a page reload

You would need to use the product id as a classname in your html and then you could do:

$.ajax({
    data: sampleData,
    type: 'POST',
    url: AjaxObject.ss_ajax_url,
    success: function(msg) {
        $( '.product-' + sampleData.productToDelete ).remove();
    }               
});

If you have any counts on the page you would need to figure that out as well. Also if you have pagination thats not generated via some javascript framework then your best bet is to just continue reloading the page as needed.