If by saving you mean save to disk, then my first question would be: Why do you want to do this for a sitemap? Just mark the url in your robots.txt file https://developers.google.com/webmasters/control-crawl-index/docs/robots_txt#sitemap

If you really need to download an xml file as in click on a link and it pops up like a normal file link does then you can Create an UmbracoSurfaceController or UmbracoApiController

And add something like this

public HttpResponseMessage DownloadSitemap()
{
    //Generate XML with XMLDocument or something else

    //Send the XML to the browser as SteamingContent
    HttpResponseMessage response = new HttpResponseMessage(HttpStatusCode.OK);
    response.Content = new StreamContent(memorySteamContainingTheXmlFile);
    response.Content.Headers.ContentType = new MediaTypeHeaderValue("application/xml");
    response.Content.Headers.ContentDisposition = new System.Net.Http.Headers.ContentDispositionHeaderValue("attachment");
    response.Content.Headers.ContentDisposition.FileName = "sitemap.xml"; 

    return response;
}

docs on surface controllers: https://our.umbraco.org/documentation/reference/routing/surface-controllers

docs on api controllers https://our.umbraco.org/documentation/reference/routing/webapi/

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