Completed tasks remain within your account until you delete them.  Here's how you can delete all completed tasks within a project.
- Select "Projects" in the left column.
 - Choose the project that you want to delete the completed tasks.
 - Filter your tasks by changing "All" to "Completed"

 - Select the wrench icon button
at the top of the task list and choose "Delete completed tasks":
 - Confirm the deletion:

 
This cannot be undone. Any subtasks will also be deleted. A record of the deletion will be listed in the Activity log, however the details of the tasks will no longer be available.