...is a physical path, but a virtual path was expected.

You already converted the virtual path to a physical path, so the second time you try the conversion fails as it already is a physical path:

protected void btnSubmit_Click(object sender, EventArgs e)
    {
        XmlDocument xmlDoc = new XmlDocument();
        string xmlPath = Path.Combine(Server.MapPath("~/App_Data"), "Sample.xml"); // The conversion is done here, by Server.MapPath
        if (!File.Exists(xmlPath))
        {
            throw new Exception("Cannot find xml file");
        }
        else
        {
            //xmlDoc.Load(Server.MapPath(xmlPath));   // Error happens here too
            xmlDoc.Load(xmlPath);                     // Same as below 
            XmlElement parentElement = xmlDoc.CreateElement("Comments");
            XmlElement name = xmlDoc.CreateElement("Name");
            name.InnerText = txtName.Text;
            parentElement.AppendChild(name);
            parentElement.AppendChild(Location);
            xmlDoc.DocumentElement.AppendChild(parentElement);
            //xmlDoc.Save(Server.MapPath(xmlPath)); // Error happens here as the path was already a physical path
            xmlDoc.Save(xmlPath);                   // Just leave out the Server.MapPath call
            BindDataList();
     }

Regards,

— Manfred