[Vuejs]-Two differed v-on:clicks within same element

You can use event modifiers with v-on:click to stop propagation of click events in your case, you can do it like following:

<div id="menu">
    <div class="menu" v-on:click="toggle" v-bind:class="{ active: isActive }">
        Hey
        <div class="m-items animated slideInRight" v-on:click.stop="change" v-bind:class="{ display: display }">
            <ul>
                <li><i class="fa fa-toggle-off" aria-hidden="true"></i>Hey</li>
            </ul>
        </div>
    </div>
</div>