You can highlight any text that includes citations, then use the Clipboard commands to Cut or Copy and then Paste it elsewhere in the document. You can do this with formatted or temporary (unformatted) citations.
To move or copy only the citation itself, make sure you highlight the entire citation (including any surrounding delimiters) as well as an extra character before and after the citation. Including the characters before and after the citation ensures that you include the hidden bookmark associated with the citation. (If the hidden bookmark is not part of the selection, you will copy plain text, and not an EndNote citation.) Then Cut or Copy and Paste it elsewhere in the document.