To empty a workspace and make it inaccessible:
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Delete all tasks and delete all projects.
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Remove yourself from the workspace.
To remove yourself: In All Workspaces View, select the appropriate workspace from the left pane and place your mouse over the workspace name to display the Edit icon. Clicking the Edit icon will give you an option to Remove Me From This Workspace. If your account does not yet have All Workspaces View, you can access this option by clicking the Gear Menu at the bottom of the workspace section.
Simply removing your own access from the workspace will remove the workspace from your left pane, but it will not delete the workspace for other workspace members.
Simply removing someone else will remove their access to any data in the workspace and will stop that person from receiving email notifications from the workspace. If someone has an email notifcation from a task in a workspace from which they've been removed, clicking the "view and edit" link will give the person an access denied message.

Email Support