html

  <textarea  ref="textarea"  v-model.trim="content"  />

js

    const put = this.$refs.textarea 
    const len = put.value.length   
    this.setSelectionRange(put, len, len)

 setSelectionRange(input, selectionStart, selectionEnd) {
      if (input.setSelectionRange) {
        input.focus()
        input.setSelectionRange(selectionStart, selectionEnd)
      } else if (input.createTextRange) {
        const range = input.createTextRange()
        range.collapse(true)
        range.moveEnd('character', selectionEnd)
        range.moveStart('character', selectionStart)
        range.select()
      }
    }