A separating system for detaching containers from a thermoformed plastic web including a first row of containers. The system includes a stamp plate and a cutting plate. The stamp plate includes a first row of stamps associated with a first set of containers from the first row of containers and a second row of stamps associated with a second set of containers from the first row of containers. The cutting plate includes a first row of cutting openings associated with the first set of containers and a second row of cutting openings associated with the second set of containers.