[Vuejs]-Is it possible to create mock api on this cypress to prevent the actual api call

You can mock it indeed. For example this mocks a server and a specific API-call:

  cy.server()
  cy.route('POST', '**/oauth/v2/token', 'fixture:/oauth/agent-token.json')

More information about route is available on the cypress site: https://docs.cypress.io/api/commands/route.html

To make sure every request is mocked, use the force404 option with cy.server:

 cy.server({force404: true})
    cy.route('**/user/jake', {user:{name:'Jake'})
    cy.visit('/')
    // your test code here

Then any XHR request to /user/jake will work, but /user/jane and /login for example, will 404