[Vuejs]-[Vue warn]: Property or method "permissionsSelected" is not defined on the instance but referenced during render

It seems like you are initializing the Vue on #app but there is no element with that id.

Try adding an id to form:

<form id="app" action="{{ route('roles.update', $role->id) }}" method="POST">

EDIT: if you want to extend an already initialized Vue instance, use Vue.extend

EDIT2: when using laravel and blade templating, to avoid these kind of issues, I would instead use a .vue file with a prop to get data inside the component and do what ever with that data inside it. In this way it is avoided multiple instantiations of Vue and the code is more granular and better structured.

if you have a vue instance in app.js or in any shared js file, delete it @Leonardo H