shabbat - Laws regarding putting someone to death for violating the sabbath

Two witnesses go to the beit din and claim that so and so violated the sabbath on a biblical level. The witnesses claim they warned him in accordance with the rules and they did their part as witnesses. When so and so is brought to beis din, he claims he did a melacha (such as digging a hole), but he claims it was for the dirt. Which would only be a rabbinical prohibition because it's a מלאכה שאין צריכה לגופה. If a person were to use this as their defense to deflect the death penalty would it theoretically work?