Fig.: to run away as fast as possible to avoid a difficult situation. It often has a negative connotation

John got behind the wheel after a lot of drinking, bumped into a parked car and, instead of facing the consequences of his bad driving, he decided to cut and run and avoid taking responsibility

John si è messo al volante dopo aver bevuto un bel po', ha sbattuto contro una macchina parcheggiata e, invece di affrontare le conseguenze della sua guida pericolosa, ha deciso di tagliare la corda per evitare ogni responsabilità

The usual bullies! They pick on the weaker kids, but when a bigger, stronger guy steps in to their defense, they just cut and run as fast as they can

I soliti bulli! Fanno i gradassi con i ragazzi più deboli, ma quando entra in scena un omaccione grande e grosso in loro difesa, tagliano la corda e spariscono a gambe levate

It is a nautical term that refers to the fastest way for a ship to start moving in the face of danger. This means that instead of raising the anchor, you cut the anchor rope and run, thus leaving the anchor behind