Removing the resistor from a diode OR gate while maintaining the ground connection results in an undefined output voltage when both inputs are low. The resistor ensures that the output remains low when inputs are at zero potential, defining the output state. In digital logic, a low output is typically considered to be in the range of 0 - 2V, with specific thresholds varying by technology, such as 0V-0.8V for TTL devices. The output is grounded through the resistor, which creates a voltage drop rather than a direct connection to ground. When calculating current, the output branch and the resistor-ground branch should be treated as parallel connections, although the voltage remains the same across both.