Hi Poni.
What you could try as well is that you change the "Publish"-field value in
the client from "Yes" to "No" for all completed tasks and then publish the
project again. Then these tasks will not appear in the My Tasks anymore.
You can write a macro for this or you can just filter for completed tasks an
change the setting manually before each publishing.
Another solution is that you change your views in the MyTasks site so that
it filters for tasks which are NOT completed.
I hope this helps.
Sylvia