You don't state if you are using the Desktop release, the Local Web-browser based release, or the Hosted Web-browser release of the Twine 2 application, and this information can effect the answer to your question.
If I understand your question correctly you are asking if it's possible to cut-n-paste the passages found on the Story Map screen from one story project to another, and the simple answer is No.
The Desktop release only allows a single instance of that application to be running at a time, so even if the application supported the cut-n-pasting of Passages in the Story Map (which it doesn't) you would also need to be running a copy of one of the web-browser based releases to do that.
In theory you can run two instances of the Web-browser release at the same time in the same web-browser, however both those instances are accessing the same local storage area (where the contents of your story projects are located), which means changes made in one instance of the application will effect the other instance which could result in interesting outcomes.
If you are willing to use command line utilities like TweeGo or grunt-entwine / twine-utils then it is possible manually manipulate the contents of a Twine 2 story project HTML file. Exactly how you would do this depends on which of the command line utilities you chose to use.
eg. TweeGo:
a. Use Twine 2's Publish to File option to create a Story HTML file for each of the Story Projects involved.
b. Use TweeGo to decompile each Story HTML file into an equivalent TWEE file.
c. Use a Text Editor to cut-n-paste the selected passasges from one TWEE file to the other.
d. Use TweeGo to generate a new Story HTML from the modified TWEE file.
e. Use Twine 2's Import From File option to overwrite the contents of the main Story Project with the contents of the new Story HTML file.