The preposition "of" is more appropriate when the meaning is "become aware," or "get to know," while "about" will tend to be used when the verb means "acquire information." Notice the difference between these two examples from the Oxford Collocations Dictionary:
Oxford Collocations Dictionary for Students of English, 2nd edition
As Gustavo has indicated with his fine explanation, it only makes sense to use "of" in your sentence, at least in a normal context. Normally, students do not become sad when they, say, learn about the demise of historical personages.
What I would like to add here is that, even with "of," the sentence is not very natural. Sentence (1) would normally be phrased by native speakers as a cleft sentence, with the "with"-phrase focused:
1a. It was with great sadness that we learned of his death.
A cleft sentence like that presupposes that you learned of his death. When speaking of someone's death, it is usual to represent matters with such presuppositions. The cleft sentence highlights the emotional dimension.
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