Once you have completed a task, you will need to mark it as completed to stop it from appearing within your tasks bar and also from appearing within the weekly task reminder emails.

To do this, click on the Tasks View (the box with the tick) at the top right of your screen  

​ 

Locate the task which you want to stop and mark it as complete, by clicking on the Completed Toggle switch:

​ 

The task will be marked as completed and then be removed from your list and no further emails will be sent.