How does the cut in voltage effects the output of a diode clipper?

For answering this question we have to consider the constant voltage drop model of the diode which says that if voltage across diode is less then its cut in voltage than assume diode to be open circuit and if it is greater then assume diode to be short circuit.

Till the input voltage is less than the cut in voltage, diode is open circuit(thus no current through the circuit). Thus entire input voltage appears across the diode as output.

When input voltage is greater than or equal to cut in voltage, then short circuit the diode. Thus, there will be no voltage drop across the diode as output.

Thus cut in voltage decides when to consider the diode open circuit and when short circuit. It decides when the diode will have output when it will not.