To archive an existing product attribute navigate to Products > Settings > Attributes to see the list of existing attributes. If there are no attributes listed you may need to create a new or restore an archived attribute. 

Once found, select Actions and select Archive. You will see that the attribute has moved from the Active to Archived section. 

It's important to note that archived attributes are not able to be selected from the product settings screens going forward but any product that already has this attribute selected will continue to use the attribute.