The Mac and iOS apps don't have an export function yet. The browser extension does, and with sync you can get everything out through it.
- Make sure sync is on in the Mac app: Settings › Subscription › Synchronize history and phrasebook. Sync needs Mate Pro.
- Install Mate for Chrome, Firefox, Edge or Opera and sign in with the same account in Settings › Pro & Sync.
- Enable sync in the extension and wait for it to finish.
- Open History or Phrasebook from the extension's popup and use the export button. You get a CSV file that opens in Numbers, Excel, Google Sheets, Anki or Quizlet.
Details and the CSV columns are in Export your History and Phrasebook to a CSV file.
You can also read, but not download, your synced History and Phrasebook at matetranslate.com/account.