"that soul shall be cut off from the midst of its people": What is the intent of this? From (Ibid.) "Those who profane it shall be put to death," I know only of one who profanes it wilfully after prior warning by witnesses. Whence do I derive (the same for) one who profanes it in and of himself? From "and it shall be cut off."
The Answer Lies in the Difference Between Two Types of Sabbath
Mekhilta Tractate Shabbata 1:19