I want to take all my submissions from last year and archive them?

We are opening up our forms yearly.  

We want to remove the old submissions so we can just see the new submissions but still somehow have the ability to see the old submissions if need be.

You can only archive the form, not the submissions. I would suggest cloning the original form and use the cloned version. This way, everything will be intact and you will start receiving new submissions to the cloned form.

http://www.jotform.com/help/27-How-to-clone-an-existing-form-from-your-account

Thanks