We see Newt Scamander use his wand several times in the film. Graves briefly mentions that Newt was expelled from Hogwarts. However, when Hogwarts students get expelled, their wands are destroyed by the Ministry of Magic.
Newt Scamander was never expelled
According to HPWiki,
In 1913, one of Leta's experiments involving a Jarvey went too far and endangered the life of a student. Rather than see his good friend expelled, Newt took the blame and was sentenced to be expelled from Hogwarts in her place. However, Albus Dumbledore, Newt's Transfiguration teacher at the time, argued strongly on his behalf and cleared his name. The expulsion was never enforced.
Even in the movie, Graves mentions how when Newt was under threat of expulsion, it was Dumbledore who saved him. Graves wonders aloud what Newt must have done to be capable of such explicit support from Dumbledore himself.
So, Newton was never expelled, nor was his wand snapped.