How can I share a large, 60 GB file with iCloud Drive?
In general, iCloud is not a person-to-person sharing platform. It is mostly restricted to sharing with your devices, so there is almost no capability to share with others. It does have the ability to share Photos and videos in a limited fashion, called 'Family Sharing". 

In El Capitan, Apple introduced a feature called Mail Drop. This feature duplicates what many have done using services such as Dropbox: it automatically uploads a large file to iCloud, and embeds a link to that file in the email message. 

If your recipient uses Apple Mail in Yosemite or El Capitan, Apple Mail automatically downloads the file from iCloud, so it looks like the attachment was sent via mail, when really only the link was sent via mail.

For more on how this works, here is the latest Apple support info.

This sounds perfect for your needs. However, Mail Drop has a limit to the file size of 5GB. It claims not to work on file sizes over 5GB (no direct personal experience). Therefore, it likely won't support your use case of 60GB.

Dropbox and Box.com do work in this manner and allow you to create both public and private links to whatever files you wish. Both offer free tiers, however, the free accounts are limited to 5GB, so your 60GB file will required a pay account.

Honestly, given the size of your file, it might be simpler, and far cheaper to put your file on a 64GB USB stick and use snail mail.