The 0.7V you're seeing is not an "error"; it's simply the forward voltage of the diode. A diode does not clip perfectly; as well as the forward voltage, there's the effective resistance.
But you can reduce the voltage offset by connecting the diode's cathode to a voltage source of -0.7V relative to 0V. In other words, disconnect the diode's anode from the 0V rail, and connect a 0.7V voltage source with its positive terminal to the 0V rail and its negative terminal to the anode of the diode.