create a new class name that does not affect the global css scope and place it in the second style tag (note that this does not have a scoped).

<Input type="textarea" class="user-defined-textarea" />
<style lang="scss" scoped>
    ...css
</style>
<style lang="scss">
.user-defined-textarea {
  textarea.ivu-input {
    border: 1px solid transparent;
  }
}
</style>

try removing scoped from style