In order to prevent a product from having broken properties all of the options for the option you wish to remove must match before the system can allow you to delete the option. For instance if I need to delete color as an option from a product and I currently have product variants with red, blue, and green, these variants must be edited to reflect the same value. This may entail deleting variants that will be identical due to editing them.

To start we need to edit our product:

Next we need to inspect our option values

We need to examine our variants and remove any that will become duplicates once our option has been removed.

After removing our variants that would be identical once the option has been removed we can now edit our product and see that we have a clickable trash icon to delete our option.

Alternately if you have many products to edit you can download your products.csv file and remove both the option name and value from the the products.