You'll need to provide a bit more detail. Do you know your Great Grandmother's maiden name? Do you know when either were born or where?
There are many Joseph Cavanagh's who have been born over the past 300 years and it is a bit hard to answer your question if it can't be established as to which Joseph Cavanagh is your Great Grandfather.
I'm sure there are many here who could help you if you could provide additional information.