Is there any way to trigger component method from parent in VueJS?

Yup, just find your component in children array, or grab it by ref attribute, and call method 🙂
ref doc

lets assume that your child component has method x.
According to documentation:

<div id="parent">
  <user-profile ref="profile"></user-profile>
</div>

var child = this.$refs.profile;
child.x();