Cut as a phrasal verb is followed by many prepositions: down, in, off, out are the commonest.

Phrasal verb Translation Examples
Cut down  Tagliare, abbattere  The tree had grown too much so it had to be cut down.
Cut down  Ridurre  To save some money you’ve got to cut down your expenses.
Cut in  Tagliare la strada  I risked an accident because a car in front of me cut in.
Cut off  Scollegare  He forgot to pay several bills so the Gas company cut him off
Cut off  Separare  Our district was cut off by the flood.
Cut out  Tagliare  To complete the poster the students have to cut out the photos and stick them to the cardboard.
Cut out  Eliminare  To get thinner you have to cut out sweets and snack.
Cut out for  Essere tagliato per  It was clear that he was cut out for a job as salesman.
Cut up Tagliare a pezzettini For a better cooking cut the meat up in small pieces.