[Vuejs]-Vue test watcher change but code inside not response

You need to set deep to true when watching an array or object so that
Vue knows that it should watch the nested data for changes.

watch: {
 getSkills: {
  handler () {
   this.list = this.getSkills.map(items => {
    return { value: items.id, label: items.name }
   })
  },
  deep: true
 }
}