Drupal 7 to 8 Migration works only on core. It doesn't migrate 301 redirects created in Drupal 7 with the Global redirect module.
Is there a way to migrate all the 301 redirects to Drupal 8 that doesn't require manually copying them after migrating the site?
The Global Redirect module doesn't store paths on a per-node basis. That's the role of the core path module which stores aliases that map to system paths in the url_alias table (in both D7/D8).
The Global Redirect module could broadly described as settings (set on its administration page) that drive logic for 301 redirecting (in a hook_init() invocation) while setting the rel="canonical" metatag (a signal that tells the search engine to index that path). Thus, there really isn't anything to migrate from the module besides various globalredirect_settings variables that store redirect settings.
That said, you can run the Migration module which will import your node path aliases (and thus the paths you're concerned with 301 redirecting to) and adjusting the settings for Global Redirect module so that it matches the settings in your D7 installation.
