What is the American version of the word ''tearaway''? (a young person who behaves in an uncontrolled way and is often causing trouble)

The word delinquent (basically standing for the legal term juvenile delinquent) is frequently used in US English in this sense. The OED has the definition

A person who commits an offence against the law or customary morality; a criminal, an offender. Now chiefly specifically: a person, especially a young person, who (persistently) commits minor crime or engages in antisocial behaviour.

Usage, from The Prime of Miss Jean Brodie:

Joyce Emily Hammond, the very rich girl, their delinquent, who had been recently sent to Blaine as a last hope, because no other school, no governess, could manage her.

Rebel is a common term for a person who resists authority, control, or convention. It can be used in a political context, but can also be used to describe a young person who flouts authority. The 1955 film Rebel Without a Cause uses the term in exactly this context, describing disaffected teenagers who act out against authority by engaging in reckless and dangerous acts.

Punk does come to mind, even though it may not be quite what you're looking for.

https://www.dictionary.com/browse/punk

Rascal, often modified as young rascal, might suffice. Note it would only really apply for minor offenses and is often used affectionately. From Merriam-Webster:

1 : a mean, unprincipled, or dishonest person

2 : a mischievous person or animal