There shouldn't be any 301 links in a sitemap. A sitemap should only contain links to active pages. So in your case, you should remove all the 301 links and replace them with the new links.
Couple notes - Having 301 links in your sitemap won't hurt your site or SEO unless the sitemap is so huge that you need to split it up into multiple files. But you should really only have the final links in the sitemap, neither people nor bots want to be redirected around. If you properly 301'd the crawlers will automatically update their links.
Changing links around in the sitemap generally won't hurt your site. Especially if the links no longer exist and you're improving the list. There are very few cases where making changes will hurt the site.