This is "Bible Stories for Adults, No. 31: The Covenant" (1989) by James Morrow. It was published in the anthology What Might Have Been? Volume 1: Alternate Empires.
The story is narrated by a robot named YHWH, who was constructed specifically to reassemble the shards of the tablets so that people might finally know God's law.
Moses initially smashes the tablets:
God has made a deep impression on the prophet. Moses is drunk with epiphany. But something is wrong. During his long absence, the children of Israel have embraced idolatry. They are dancing like pagans and fornicating like cats. They have melted down the spoils of Egypt and fashioned them into a calf. Against all logic, they have selected this statue as their deity, even though YHWH has recently delivered them from bondage and parted the Red Sea on their behalf.
Moses is badly shaken. He burns with anger and betrayal. “You are not worthy to receive this covenant!” he screams as he lobs the Law through the desert sky. One tablet strikes a rock, the other collides with the precious calf. The transformation is total, ten lucid commandments turned into a million incoherent shards. The children of Israel are thunderstruck, chagrined. Their calf suddenly looks pathetic to them, a third-class demiurge.
The laws are lost:
The survivors beseech Moses to remember the commandments, but he can conjure nothing beyond, “You will have no gods except me.” Desperate, they implore YHWH for a second chance. And YHWH replies; No.
Thus is the contract lost. Thus are the children of Israel fated to live out their years without the Law, wholly ignorant of heaven’s standards. Is it permissible to steal? Where does YHWH stand on murder? The moral absolutes, it appears, will remain absolute mysteries. The people must ad-lib.
They try to reconstruct the laws:
The work is maddening. So many bits, so much data. Shard 76,342 seems to mesh well with Shard 901,877, but not necessarily better than with Shard 344. The fit between Shard 16 and Shard 117,539 is very pretty, but ...
Thus does the ship of humanity remain rudderless, its passengers bewildered, craving the canon Moses wrecked and YHWH declined to restore. Until God’s testimony is complete, few people are willing to credit the occasional edict that emerges from the yeshivas. After a thousand years, the rabbis get: Keep Not Your Ox House Holy. After two thousand: Covet Your Woman Servant’s Sabbath. Three hundred years later: You Will Remember Your Neighbor’s Donkey.
The robot YHWH succeeds in reconstructing the tablets, but the robot SATAN convinces YHWH that revealing the laws will now only cause grief (which God? which sabbath?) and ultimately YHWH commits suicide to irretrievably destroy the tablets.