"It is not my cup."
Translation:Ce n'est pas ma coupe.
Coupe does mean cut. Couper is the verb "to cut". Coupe can also mean haircut/hairstyle. I would not have used "coupe" here, but "tasse" instead. The only time I've heard "coupe" used as "cup" is in hockey for the Stanley Cup - "La Coupe Stanley". But I am not a native speaker. Maybe it is more common in France to say coupe.