Dawid was the older of two sons born to Jewish parents in Warsaw. His mother supported the family by selling women's clothing. Dawid's father wrote for the Yiddish newspaper Haynt and the journal Literarishe Bleter. The Szpiros lived in the heart of Warsaw's Jewish district, where Dawid and his brother, Shlomo, attended Jewish schools.
1933-39: Dawid graduated from a trade school at the age of 17 and began working as a mechanic. When his father took a job in Argentina in 1937, Dawid and his brother sent clippings from local antisemitic publications to persuade their father to resettle the family in Argentina. But Dawid's father did not believe that Polish Jews were in danger and returned to Poland in 1938. That year, Dawid joined the Zionist organization, Ha-Shomer ha-Za'ir. The Germans occupied Poland in 1939.
1940-44: In November 1940 the Jewish ghetto in Warsaw was sealed off. Dawid and his family obtained sufficient food by exchanging clothes they had sewn at home for food brought by Poles from outside the ghetto. Dawid worked together with other Ha-Shomer members in the ghetto to forge and deliver false papers. In 1942 he was smuggled to Tarnow, where he lived secretly in a non-Jewish section of the city. While there, Dawid obtained false papers for his mother, who had escaped the Warsaw ghetto, and for his brother, who was in a nearby labor camp.
Dawid and the other resistance members with whom he lived were discovered by the Gestapo and tortured to death. His brother and mother were the only members of the family to survive the war.