There is a complete API to export all the survey data (as much or as little as you please). The output will be in the JSON format.
In your case, the way it works is you first download a list of survey IDs (get_survey_list). Note that these are not the same as the survey code that is part of the web address you've sent to respondents. After you have retrieved the survey IDs, you can retrieve survey details (get_survey_details) by passing the API the survey ID.
You have to register on the developer site and also request an API key and authentication token. This can all be done in the browser if you aren't familiar with programming.
You can also download from the API from a browser using the API Console.
If you are comfortable with python, or want to learn, you can find some pre-programmed stuff here: https://github.com/SurveyMonkey/python_guides
You can also use curl to access the survey data.