Newt Scamander was expelled from Hogwarts after he took the blame for someone else's crime. A similar thing happens to Hagrid and his wand was snapped. However Newt still has his wand.
How & why?
Why wasn't his wand snapped?
A MACUSA document in an official companion book shows Newt was never actually expelled from Hogwarts. Dumbledore defended him and his name was cleared before he was expelled, so his wand would not have been broken.
NOTES: Proposed expulsion from Hogwarts School of Witchcraft and Wizardry due to the illegal possession of a magical beast causing endangerment of human life and violation of animal welfare laws 101/304.
Magical Beast: Jarvey, Level 3
Punishment: Expulsion from Hogwarts School of Witchcraft and Wizardry.
– The expulsion was never enforced - Hogwarts Professor Albus Dumbledore defended Newton resulting in his name being cleared.
– The Ministry of Magic Animal Welfare Department were also informed of the violation and required to rehouse the magical creature.
-The Case of Beasts: Explore the Film Wizardry of Fantastic Beasts and Where to Find Them
This is similar to when Harry was almost expelled, but was never actually expelled because Dumbledore defended him. Harry was very close to expulsion. He received a letter from the Ministry expelling him, which also mentioned destruction of his wand.
“We have received intelligence that you performed the Patronus Charm at twenty-three minutes past nine this evening in a Muggle inhabited area and in the presence of a Muggle.
The severity of this breach of the Decree for the Reasonable Restriction of Underage Sorcery has resulted in your expulsion from Hogwarts School of Witchcraft and Wizardry. Ministry representatives will be calling at your place of residence shortly to destroy your wand.”
- Harry Potter and the Order of the Phoenix, Chapter 2 (A Peck of Owls)
However, due to Dumbledore’s defense of him, Harry was proven innocent and never expelled, so he continued to attend Hogwarts with no gap in his studies. Dumbledore also reminded the Minister of Magic that the Ministry cannot confiscate wands until charges were successfully proven.
“But, as the Ministry has no authority to punish Hogwarts students for misdemeanours at school, Harry’s behaviour there is not relevant to this hearing,’ said Dumbledore, as politely as ever, but now with a suggestion of coolness behind his words.
‘Oho!’ said Fudge. ‘Not our business what he does at school, eh? You think so?’
‘The Ministry does not have the power to expel Hogwarts students, Cornelius, as I reminded you on the night of the second of August,’ said Dumbledore. ‘Nor does it have the right to confiscate wands until charges have been successfully proven; again, as I reminded you on the night of the second of August. In your admirable haste to ensure that the law is upheld, you appear, inadvertently I am sure, to have overlooked a few laws yourself.”
- Harry Potter and the Order of the Phoenix, Chapter 8 (The Hearing)
The charges against Newt were never successfully proven, so the Ministry could not destroy his wand.
Apparently, "all will become clear". Or so says J.K. Rowling.
The truth is, as for now we don't know why Newt apparently gets to keep his wand, even after expelled. There are some fan theories, but nothing official.
Q. Why was Newt allowed to keep his wand & do magic, and work for the ministry? Hagrid had a different experience after expulsion..
J.K. Rowling: All will become clear. Trust me.