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 surrounding delimiters). Then Cut or Copy and Paste it elsewhere in the document.
Note:
Some issues may arise when you use the Cut, Copy, and Paste commands in a document with Track Changes turned on. If this occurs, turn off Track Change when you use these edit commands.