Short answer
Open "Manage Index" under "Index Management", click the red trash can next to the Index, then confirm delete.
Full explanation
Go to "Index Management" on the left hand side of the Ask Screen
Select "Manage Index" from the Menu.
Find the Project you want to remove.
Click the red Delete (trash can) button on the right.
Read the confirmation and select Delete to finish.
Deleting a Project permanently removes its files and folders, Semantic Map, Email-to-Project settings, and chats tied to that Project. 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 a Project.
Collections provided by AskTuring cannot be deleted by users.