In 60 AD, there were already very large Jewish neighborhoods in Egypt (Alexandria and Elephantine), Libya ("Cyrene" in the New Testament), Caesarea (coast of Israel), Damascas, Antioch, Tarsus, and many cities in Asia Minor.
Before any "expulsion" took place, there was wide-spread anti-Semitism, worse than that of WW II in that half the Jews in the Roman world were killed, probably more than 2 million in Jerusalem alone. During the war between the Romans and Jews within Judea and Galilee (60-72 AD, if you count the cruel procurators and the holdout at Masada), there were also public attrocities against Jews in other cities, like Alexandria, Antioch and Damascas, where tens of thousands of Jews were simply butchered, many by citizens, not by armies of Rome, and with apparent "official" blessing.
So the "expulsion" and "diaspora" were an amalgum of events, you really can't pin them down to any single cause.
If you don't mind very lengthy and difficult reading, find Josephus "Wars of the Jews" on line. Here are two links that I use:
http://www.ccel.org/j/josephus/JOSEPHUS.HTMhttp://wesley.nnu.edu/noncanon/pseudepigrapha.htm(Josephus' description of the war, especially in Jerusalem, is lengthy and very graphic.)