I think others might find this helpful. For those of you that are looking to get rid of tasks in a projects, but would rather not mark complete, I have a possible solution. Possibly because you are setting up your reports a certain way or you have a catch all project that keeps getting more tasks throughout the year that you would like to clean up occasionally. Even though Asana does not currently have a feature to archive a task you actually can. What you would need to do is create and archive a project for the sole purpose of collecting archived tasks. When you have completed a task that you would like to archive, rather than marking complete, move the task from the current project into the archived project. The task will no longer appear in the current project or your My Task section, yet it will come up still in your reports.
I hope you find this tip helpful,