this.$refs.swiper.swiper.slideTo(2, 500, false);

<template>
  <div>
    <swiper ref="swiper"
            :options="swiperOption"
            style="height:100px">
      <swiper-slide v-for='(item,index) in newObjData'
                    :key="index">
        <li v-for='(item,index) in newObjData[index]'
            :key="index">
          <span>{{item.id}}</span>
          <span>{{item.name}}</span>
          <span>{{item.age}}</span>
        </li>
      </swiper-slide>
    </swiper>
    <button @click="switchPage">切换页码</button>
  </div>
</template>

switchPage () {
 this.$refs.swiper.swiper.slideTo(2, 500, false);
},