Slicing up an image into rows and columns in Java
Not sure I understand your problem but what about changing the signature of you constructor to:

GridImage(String path, String filename, int rows, int columns)


And have path and filename be attributes of your object.

I don't know why you implemented it as a runnable, but then I would also put all the code in the run method (starting with loading the file)...

OK I got what you are asking now, do the following:

File originalImage = new File(filename);
String path = originalImage.getPath();
String fileName = originalImage.getName();


Now you have all you need to create your new files.

BTW: have a look at the File javadoc...