バージョン

nuxt3, vuetify3

"nuxt": "^3.2.3"
"vuetify": "^3.1.7"

実装

sample.vue

<template>
  <v-radio-group v-model="hoge" @click="clearRadioSelected($event, 'hoge')">
    <v-radio label="はい" value="1"></v-radio>
    <v-radio label="いいえ" value="2"></v-radio>
  </v-radio-group>
  <v-radio-group v-model="fuga" @click="clearRadioSelected($event, 'fuga')">
    <v-radio label="YES" value="1"></v-radio>
    <v-radio label="NO" value="2"></v-radio>
  </v-radio-group>
</template>

<script setup lang="ts">
const hoge = ref();
const fuga = ref();
const clearRadioSelected = (event: Event, target: string) => {
  if (event.target instanceof HTMLInputElement && event.target.type === "radio" && event.target.tagName === "INPUT") {
    const value = event.target.value;
    switch (target) {
      case "hoge":
        hoge.value = value && value === hoge.value ? undefined : value;
        break;
      case "fuga":
        fuga.value = value && value === fuga.value ? undefined : value;
        break;
    }
  }
};
</script>