function AddCountry(element) {

    var oldSelect = jQuery("select[name='investor-country[]']").last();
    var newSelect = jQuery(oldSelect).clone();

    // Remove previously selected option
    var selected = oldSelect.val();
    newSelect.find("option[value="+selected+"]").remove();

    jQuery(element).before(newSelect);
}

選択したオプションを削除する別の方法:

newSelect.find('option').eq(oldSelect[0].selectedIndex).remove();

これを試して：

    //get the selected value
    var val = $("select[name='investor-country[]']").val();
    //get the selected option
    var option = $("option[value="+val+"]");
    //append the selected country somewhere
    $('#selected').append('<span>'+option.text()+'</span> ');
    //remove the selected option
    option.remove();

デモ