Not possible. A portlet is not a servet - it cannot stand on its own - it needs run within the context of the portal.
You could refactor all of your code into pojos and front that with a servet and a portlet. Then you could access the servlet to get at the data. You could even use the same jsp to display the data. Though you will have to be careful of links and post uris - you will have to generate the uris for those in the portlet and servlet and pass them to the jsp.
Alternately, you could define a new layout that consists of only a single portlet.
Basically what I would like to achieve is to be able to refresh a single portlet inside a page without refreshing the whole page. additionally I would like to be able to trigger that refresh through a JS method.
According to the documentation pages can be ajaxfied and support this behavior. I assumed thought, that it meant that the portal somehow does acquire the content of that single portlet and then it replaces the Inner HTML of the portlet window or use some other technique . sadly, I did not find any technical explanation how this is achieved.
Do you know how does the partial refresh work?
It usually helps to describe what you are attempting to achieve because as you can see, my answer to your original question did not help you in the least. And unfortunately, I have not used ajax with the portal so cannot help you there either.