If you are using a version of SSI Web earlier than version 8, then there really isn't a great way to automate the process. Previous versions stored respondent data in multiple files, so you would need to somehow crawl each of those files and store the information you parsed into your database. Figuring out how to use existing tools, like exporting from SSI Web to CSV like Paul mentioned, are probably the best approach.
In version 8 we are now using a database, so I would imagine it would be possible to query our own table for a particular survey and write that information to another table or database. I don't know the best way or language to use to do that, but it seems like it should be doable.