Loop certain number of times then do action

Now I am even more confused because nothing in the sketch that you have posted outputs anything to cutPin

You could do something like this

void loop()
{
    int relayState = digitalRead(relayPin);
    if (relayState == HIGH)
    {
        for (int i = 0; i < numberOfSteps; i++)
        {
            digitalWrite(stepPin, HIGH);
            delayMicroseconds(100);
            digitalWrite(stepPin, LOW);
            delayMicroseconds(100);
        }
        digitalWrite(cutPin, HIGH);
        delay(100);
        digitalWrite(cutPin, LOW);
    }
}

but I don't know what you actually want to do to cutPin