If asked to provide separate list of publications in addition to CV, should CV still include list of publications? I am applying for an assisstant professor position, and asked to provide a CV, as well as a separate list of publications. Should I still keep a "publications" section in the CV, or refer to the separate list by writing something like "see enclosed list of publications"?
Yes, I would say so.  A CV always should list publications.

It may be that for some reason to do with their search process, they find it convenient to have a separate document that only lists publications, rather than digging through the CV to find it.  But that doesn't mean you should remove this list from the CV.