How can I update sitemap.xml?

You don't need to update your sitemap manually.

All Shopify stores automatically generate a sitemap.xml file that contains links to all your products, product images, pages, collections, and blog posts. This is used by search engines like Google and Bing to quickly scan your webpages for content. if your store is www.mystore.com, you can check your sitemap at www.mystore.com/sitemap.xml. It's basically a file read by the Google search robots.

What is "Sitemap"?

This sitemap file that Shopify generates links to separate sitemaps for your Products, Collections, Blogs, and Pages. The sitemap will be updated by Shopify automatically whenever you add a new page/product/image/collection/blog post on your Shopify store. Once your sitemap is submitted, Google will try to look for the changes whenever your site is changed. This can keep Google notified for your latest website version.

How can I submit my sitemap to Google?

You can follow the instructions here to verify your site and submit your sitemap: https://help.shopify.com/manual/using-themes/find-site-map. After you submit for the first time, Google will read it automatically after that.

Can I notify Google to scrape my latest sitemap?

Yes! If you update your store and you would like Google to update the index, you can manually notify Google to scrape again. Just visit SPO => Setting Tab => Press "Submit Now" button next to Sitemap. A new tab will be opened and you'll see the message from Google.

Reference:
1. Find and submit your sitemap - https://help.shopify.com/manual/using-themes/find-site-map
2. Verify your site for Google Search Console - https://help.shopify.com/themes/customization/social-media/verify-domain-with-third-party-services
3. Google Search Console (Previously known as Google Webmaster Tools) - https://www.google.com/webmasters