Currently the best and easiest way to bulk add or remove your variants would be via our CSV file. We do have the option to bulk delete products in your bulk editor but this is only at the product level and not done by variants.
If you have not already, you can take a look at our CSV guide along with our CSV template here: https://docs.shopify.com/manual/products/import-export
If you are looking to bulk edit your variants we do have a great app which can allow you to do this called Bulk Edit - https://apps.shopify.com/bulk-edit
I hope that helps and best of luck to you!
Here is the proper and complete method to remove variants via the CSV export/import feature:
You must delete every unwanted variant row in the CSV, but if you only had 2 variants to start with and you remove one, you will need to set the cells in the Option1 Name column to "Title" and Option1 Value to "Default Title" (do not include the quotes).
If you leave those columns blank (as you might think to do, in order to not have any variants), you will get an import error (the error notification is emailed to you, so you will have no idea on the actual web page after uploading that there were any errors, which is SUPER confusing).