There are several ways to remove a project from a view in the Project Center, this could be via custom fields or the security model. High level these are described below:
You could have an Enterprise Custom Field that is link to a Look up table. The field could be called "Project Status" and the values in the look up could be "Draft", "Live", "Completed", "Archived". Then set filters on the Project Center views to filter out where the "Project Status" field = "Archived"