Use the key modifier on the el-popover as the element should be recreated
The key special attribute is primarily used as a hint for Vue’s virtual DOM algorithm to identify VNodes when diffing the new list of nodes against the old list. Without keys, Vue uses an algorithm that minimizes element movement and tries to patch/reuse elements of the same type in-place as much as possible.

Example:

HTML

<el-popover 
   :key="trigger"
    placement="top-start"
    :trigger="trigger"
    width="200"
    :title="title"
    :content="content">
    <el-button slot="reference">Button</el-button>
 </el-popover>

 <el-button type="text" @click='changeToClick'>Change To Click</el-button>
  <el-button type="text" @click='changeToHover'>Change To hover</el-button>

Javascript

data() {
        return {
          visible: false,
          title: 'Default title',
          content: 'Default content',
          trigger: 'click',
        };
      },
      methods: {
        changeToClick() {
          this.title= 'Click title';
          this.content= 'Click content will be here';
          this.trigger  = 'click';
        },
        changeToHover() {
          this.title= 'Hover title';
          this.content= 'Hover content will be here';
          this.trigger  = 'hover';
        },
}

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