Jewish traditions were handed down and taught by the Torah-sages in the yeshivas, just as had been done prior to that time.
The same way that they had survived until that time: through the continued handing down of Jewish traditions (the Torah) among the sages and their disciples, and the Jewish communities in general. Specifically, the year 132 CE was about the time that Rabbi Akiva died. His greatest disciples (Rabbi Meir, Rabbi Yehuda, Rabbi Yossi, Rabbi Shimon bar Yochai and Rabbi Nehemiah) each headed a yeshiva (Torah-academy) of his own, and (as well as teaching) they strived to lead the Jewish communities through the hard times (132 CE was around the time of the Roman destruction of the city of Beitar).
The first Jewish Diaspora was the forcible exile to Babylon in 586 BCE. However, the famous second Jewish Diaspora happened under the Romans from 70 CE to 132 CE. Jewish Zealots had fought the Romans on these two occasions and the Romans had enough of it. The Romans realized that the Jews had a fundamental connection to the land, so separating them from it and from each other would make them more docile. As a result, the Romans evicted the majority of Jews from the province of Syria-Palaestina.
Rashi a Jewish sage died
There have always been Jews in Palestine. They were not the majority between the years 132 CE and 1949 CE.
Rashi a Jewish sage died
What is the answer
The Talmud
After the Romans sacked Jerusalem in 70 CE. they are reported to have sold many women and children into slavery. Again, after the Jewish revolt of 132-135, the Romans sold many defeated Jews as slaves.
Toledo is one example.
The first Jewish-Roman War (years 66-73 CE), sometimes called The Great Revolt (Hebrew: המרד הגדול‎, ha-Mered Ha-Gadol), was the first of three major rebellions by the Jews of Iudaea Province against the Roman Empire (the second was the Kitos War in 115-117 CE, the third was Bar Kokhba's revolt, 132-135 CE). It began in the year 66, stemming from Greek and Jewish religious tension.[1] It ended when legions under Titus besieged and destroyed Jerusalem, looted and burned Herod's Temple (in the year 70) and Jewish strongholds (notably Gamla in 67 and Masada in 73), and enslaved or massacred a large part of the Jewish population. The defeat of the Jewish revolts by the Roman Empire contributed substantially to the numbers and geography of the Jewish diaspora, as many Jews were scattered or sold into slavery after losing their state.
There was no single leader of Jewish people after the year 70 CE.
Shabbetai Zevi. He was one of the Jewish false messiahs.