It should be turned on by default, but if you have disabled it at some point, this may be the reason why the feature doesn't work for you. In order for the Translate history service to work, you must have the Web & App Activity setting enabled on your profile's settings page. If you are not logged into a Google account but want to remove the saved history, you simply need to go to the History section of the Google Translate app, tap on the three dots located on the upper right side, and choose, 'Clear all history.' You can even set up an auto-delete interval if you want the service to delete your activity automatically. There you can choose to delete the saved history from today, from a custom range, or from all time. The app will take you to your account's Google Translate history page.
If you want to delete your Google Translate history on your account, go to the app's settings and tap on the 'Manage activity' button. But you should know that even if you aren't logged into the Google Translate app, it still saves a history of your searches locally on your device. If you don't want the app to save your translations to the cloud, you can simply choose the 'Use Translate without an account' option or later log out of your Google account.