The paste command is commonly represented by a clipboard with a document in front of it. The cut-and-paste metaphor originates from traditional manuscript editing, where people would actually cut paragraphs of text and paste them on another paper.
The cut-and-paste commands were part of the Xerox text editors in 1974. Apple Lisa was apparently the first operating system to use the term clipboard and the paste icon appears at least in the 2.0 version of Microsoft Word that was released in 1991.
Microsoft Word 2.0 1991.