Can I be a Slovak Citizen?

I want to be a citizen of the EU so that I can live in Europe later in life. The only way I can think of to do this would be hereditarily through my Grandfather. My Grandfather's parents were citizens of Slovakia and came to America through Ellis Island. Can he get his citizenship, then in turn, my mother get her citizenship, and then finally I get my citizenship? I haven't really found any scenario like this on any website I looked at. Please Help!