Remember the Sabbath day to sanctify it. Six days shall you work and you did all your melachah; but the seventh day is Shabbat to Hashem, your G-d; you shall not perform any [acts of] melachah--you, your son, your daughter, your slave, your maidservant, your animal, and your convert within your gates--for in six days Hashem Made the heavens and earth, the seas and all that is in them, and He Rested on the seventh day. Therefore, Hashem Blessed the Sabbath day and Sanctified it. (Exodus 20:8-11)
Exodus 31:12-17 Hashem Said to Moses, Saying: "Now you speak to the children of Israel, saying: 'However, you must observe My Sabbaths, for it is a sign between Me and you for your generations, to know that I Am Hashem, Who Makes you Holy. You shall observe the Sabbath, for it is Holy to you; its desecrators shall surely die, for whoever does melachah on it, that spirit shall be cut off from among its people. For six days melachah will be done but the seventh day is a day of complete rest, it is Sacred to Hashem; whoever does melachah on the Sabbath day shall surely die.' The children of Israel shall observe the Sabbath, to make the Sabbath an eternal Covenant for their generations. Between Me and the children of Israel it is a sign forever that in a six day period Hashem Made the heaven and the earth, and on the seventh day He Rested and was Refreshed."
Acts of melachah are Forbidden on Shabbat. Melachah is not work, it is "kingly acts;" acts of creation. Therefore, acts of creation are Forbidden on Shabbat, for Shabbat is a day of complete Rest for Hashem, the Judge of Israel. It is a day when the people of Israel cease to serve their flesh, and their spirits are refreshed with rest. This is a testament to the Redemption of Israel, for G-d Freed His people from the bondage of egypt and Made them into a nation of G-d, that lives according to the Spirit of G-d. The people cease to create on Shabbat, so that they might look over their creations and judge what was made, thus judging their actions and observing the consequences of their behavior. It is a day of rest, that they can enjoy their creations and the Creations Made for them, that they should not be slaves, and should live for themselves according to the spirit that is theirs. That way they will know what was done and what should be done, and will behave Reasonably in the next week of creation--for all generations.
Those who would desecrate the Sabbath day and perform acts of creation in defiance of their G-d, are the ones who would defy their Judge and break His Laws. When G-d Told Adam not to eat from the Forbidden tree, for he would surely die, G-d did not lie. But Adam disobeyed G-d and ate the Forbidden fruit, and yet he "lived!" But ask yourself what life is. For the life of man is of the Breath of G-d. Those who turn back from the Reason of their spirits, and stray from the Spirit of G-d, are not exactly living the life they were Given. These people corrupt themselves, living according to the dust of their flesh and the desires of their hearts, and become the slaves of their bodies--living like the animals. The dust of man was Redeemed with the Spirit of G-d, for we were Created in the "Image" of G-d! To defile the spirit that is in you and enslave yourself, is a death in itself--for dust is what you will become and dust will be your end.
Those who are not conscious of their actions and don't rest to judge the consequences of their behavior, lose control of themselves and lead themselves into corruption and death. There's no need to even kill these people, for they are a living death. However, these people don't belong in Israel and their defiance cannot be tolerated. Should they act unknowingly and defy G-d unintentionally, then they should be given a chance to redeem themselves--for G-d does not seek to make slaves of His people. But should they act knowingly and defy G-d intentionally, then this rebellious act will end for them in death.
To read more on this topic visit Shabbat in the Laws of G-d.