You can delete individual variation child products the same way you delete any other product. To create a new set of variations, you will have to create a new product. You can start by copying the mother product (it will not copy the variation children) so you can start with the mother product again, make any necessary edits to that new mother product, and recreate your variations under the Variations tab of the Edit Product screen.
Once you have created a new mother product, you can create your new variation option sets under the Variations tab by clicking the plus sign in the "Variation Options" panel. We will look into adding other ways to access that page as we plan the next few upcoming versions!