Styleguide owners can delete styleguides directly from their workspace, under Styleguides Tab. Hover over a styleguide and select “Delete Styleguide…” under the Settings menu.
Type the styleguide name you want to delete and click on the “Delete” button:
Once a styleguide that is linked to a project is deleted, the colors, text styles and components inherited from that styleguide will be removed from the project. If it's a child styleguide though, you'll keep seeing the parent styleguide data.
☝️ Deleting a parent styleguide only deletes that specific styleguide, not the child styleguides. Once a styleguide is deleted it can not be recovered.