It should be possible to "Reject" the ideas, like the same way as on today it is possible to "Graduate" the ideas. The idea will be still visible in the community but with a "Rejected" symbol (the same way it is now with the Graduated symbol)
The sequence can be:
# The community owner can "Reject" an Idea
# He/ She is asked to provide the reason for the Rejection
# The "Rejected" symbol appears with the idea (see screenshot as an example)
# The reason given by the owner is visible as a comment
The first 2 steps is possible as on today (Thx to Ergin for finding this), but the moment the owner rejects an idea, it is no more visible on the Ideation blog.