I created a self-closing modal using a watcher, code below:

     <mdb-modal :show="showModal" @close="showModal = false">
        <mdb-modal-header>
          <mdb-modal-title>Modal title</mdb-modal-title>
        </mdb-modal-header>
        <mdb-modal-body>...</mdb-modal-body>
        <mdb-modal-footer>
          <!-- <mdb-btn color="success" @click="showModal2 = true">Show modal 2</mdb-btn> -->
          <mdb-btn color="secondary" @click="showModal = false">Close</mdb-btn>
          <mdb-btn color="primary">Save changes</mdb-btn>
        </mdb-modal-footer>
      </mdb-modal>

 data() {
    return {
      showModal: false,
    };
  },
  watch: {
    showModal(value) {
      if (value) {
        setTimeout(() => {
          this.showModal = false;
        }, 1000);
      }
    }
  }

Let me know if this approach solves your issue. Kind regards, Magdalena