Short answer
Open Manage Index, click the red trash can next to the Index, then confirm delete.
Full explanation
Go to Manage Index from the left menu.
Find the Index you want to remove.
Click the red Delete (trash can) button on the right.
Read the confirmation and select Delete to finish.
Deleting an Index permanently removes its files and folders, Semantic Map, Email-to-Index settings, and chats tied to that Index. This cannot be undone.
Tips
Make a local copy of any files you may need before deleting.
You need the Manage Index permission to delete an Index.
Shared Indexes provided by AskTuring cannot be deleted by users.