[Vuejs]-How to use put methode on vue js + node

TL; DR; You need to send an AJAX request from your client application.

The main problem is that the Vue.js code has nothing to with the back-end code. And the Vue.js application lives in the browser. So the right way to do that will be to define a click handler that will collect the data from a form and then send the AJAX request to the Node.js server on the endpoint that handles user update.