“Now it came to pass when he drew closer to the camp and saw the calf and the dances, that Moshe’s anger was kindled, and he flung the tablets from his hands, shattering them at the foot of the mountain.”(32:19)
How could Moshe break the tablets which contain Hashem’s name? Is there not an explicit prohibition to erase or destroy Hashem’s written name?
The Rokeach explains that when Moshe drew near to the camp the letters flew off the Luchos. This annulled their sanctity and he was allowed to break them. Moshe’s intent was to save them from sinning.
The Chasam Sofer asks why didn’t Moshe break the luchos immediately when he heard they had sinned? Based on the above the answer is clear. Moshe could not break the luchos because they contained Hashem’s name. Only when the letters flew away could he throw them down.
But why did the letters only fly away when Moshe approached the camp and not immediately when Hashem told Moshe about the sin? The verse emphasizes that the luchos were formed and written upon by Hashem. This is to teach us that when Moshe approached the place of impurity of the sin of the golden calf, the holy letters flew away. Only then could he break them. (Chavelets Hasharon)