First of all, we recommend to use two-way data binding v-model instead of manual options applying. Here's an example code:

<mdb-select
  v-model="basicOptions"
  placeholder="Select an option"
  label=""
/>

and data:

data() {
  return {
    basicOptions: [
      { text: "Option nr 1", value: "Option 1" },
      { text: "Option nr 2", value: "Option 2" },
      { text: "Option nr 3", value: "Option 3" }
    ]
  };
}

After each change, picked option gets and attribute selected. You can easily get the selected item by filtering options (in this case it would be basicOptions).

Best regards