So it depends on what you mean by "exile". It's relatively clear that
some people were displaced. Josephus references 90,000 people being brought to Rome after the Great Jewish Revolt. And during the war it's exceedingly likely that at least
somepeople fled the conflict to more peaceful areas. There are references to some Sicarii escaping to Egypt, for example. No one bothered to figure out how many, but some people were definitely displaced.
There wasn't an exile in the total sense, since Jews were still allowed to live in Judea. That's not really disputed by anyone's narrative--there were enough Jews in Judea for another revolt in 135, and Jewish texts were still being written, mostly in the Galilee, even after 135.
But what is clear is that the community began a substantial decline after 70. Gradually the religious centers, where big-time books were written, moves to Babylonia, which had already had a Jewish community for centuries.
So at least some Jews were forcibly displaced, and it's likely a number more fled the conflict. That goes for both 70 and 135. This wasn't the beginning of the diaspora, since there were substantial communities of Jews living elsewhere from earlier. In fact, the majority of Jews probably migrated voluntarily, rather than being forced out, though forcible expulsion did occur1 . But many Jews were forcibly removed as slaves in large numbers, both after the revolt in 70 and in 1352 .
- Gruen, Erich S. "Diaspora--Jews Amidst Greeks and Romans"
- Smallwood, Mary E. "The Jews under Roman Rule". One interesting tidbit from this book is that after the revolt in 135, the market was flooded with Jewish slaves, such that they had no more value than a horse.