You'll need a full trust form, and then you can add some code to the OnSubmitRequest event handler which writes out the file to their drive.

It might be easier to simply instruct the user (and add instructions to your form) to save the form to their computer when they are done submitting it.

Is it possible? I've made the form for students to fill out. When they hit
submit I want the data dumped into a .txt or .xml file in a folder on their
own computer.