I want to keep the autogenerated sitemap.xml on a different server.
Will google follow 301 redirect while trying to fetch sitemap.xml?
I am not sure if Google will follow the 301 (It probably will). However, the safer choice is to add the new link of the sitemap.xml in your robot.txt like this:
User-agent: * Allow: / Sitemap: http://www.example.com/sitemap.xml
You can read more about it here: https://support.google.com/webmasters/answer/6062596?hl=en