Controlled menu 
Control the menu open state programmatically with the isMenuOpen prop.
Demo source-code 
vue
<script setup lang="ts">
import { ref } from "vue";
import VueSelect from "vue3-select-component";
const selected = ref("");
const isMenuOpen = ref(false);
</script>
<template>
  <button type="button" @click="isMenuOpen = !isMenuOpen">
    Toggle menu ({{ isMenuOpen ? "opened" : "closed" }})
  </button>
  <VueSelect
    v-model="selected"
    :options="[
      { label: 'Option #1', value: 'option_1' },
      { label: 'Option #2', value: 'option_2' },
      { label: 'Option #3', value: 'option_3' },
    ]"
    :is-menu-open="isMenuOpen"
    @menu-opened="isMenuOpen = true"
    @menu-closed="isMenuOpen = false"
  />
</template>