For the personal board you can remove a task by:
Changing the task assignee
Snoozing the task
Marking the task as completed
Marking the task as canceled
For the subject board you can remove a task by:
Unshare the task on that subject
Marking the task as completed
Marking the task as canceled
You can also always delete a task, though we recommend marking it as canceled to keep a record it existed, and was discarded for a reason.