You can use scope slots to achieve this:

<date-picker
  format='MM-DD-YYYY'
  value-type='format'
  v-model='time'>
  <template #input='{ props, events }'>
    <input
      v-bind='props'
      v-on='events'>
  </template>
</date-picker>

Now we can intercept input events and remove unwanted characters:

<date-picker
  format='MM-DD-YYYY'
  value-type='format'
  v-model='time'>
  <template #input='{ props, events }'>
  <input
    v-bind='props'
    v-on='{
      ...events,
      input: event => handleInput(event, events.input)
    }'>
  </template>
</date-picker>

...
  methods: {
    handleInput (event, update) {
      let value = event.target.value.replace(/[^0-9/-]/g, '')

      // 强制Vue在删除一些字符后刷新输入框
      this.$forceUpdate()

      // 将新值应用于让vue2-datepicker继续其流程
      update(value)
    }
  }
...

Example