Sorry, there is not a directly way you can cache the result in Translator API, but you can create some logic to do it.
One thing you can do is using Azure Logic App to connect the result file with the API, check in the cache first then do the translate. https://azure.microsoft.com/en-us/services/logic-apps/#features
One sample by creating customized logic :https://stackoverflow.com/questions/62802736/azure-translation-api-caching
Regards,
Yutong