The hand and heart referred to are the symbolic representations of the emotions of Ozymandias, the Egyptian king whose image was captured in the now-fallen sculpture. The traveller states that the sculptor read the emotions of the ancient king well and reflected them in the facial expression of the statue. Thus the "sneer of cold command" that the face of the statue depicts shows the "passions" that motivated the ruler's hands and heart. Just by looking at the facial expression, the traveller discerns that the king had a "hand that mocked them." In other words, he did not have kind and giving hands, or hands that protected his people. He reached his hands out in mockery, confirming to his subjects that they were worth little or nothing compared to his grandeur. Likewise, he had a "heart that fed." It was not a compassionate or loving heart, but one that preyed on his people, using them for his own gain and to satisfy his own desires. Interestingly, the parts of the statue that seem to be missing are the parts that contain the hands and the heart. The image is "trunkless." The head is visible, "half sunk," and the legs are still standing. But the traveller is able to extrapolate the missing pieces, the hand and the heart, from the expression the sculptor carved into the face.
The poet is saying that the stone facial expression showing the passions of Ozymandias has survived long after both the tyrant and the sculptor are gone. The “hand that mocked them” (meaning the passions depicted on the shattered visage) is the sculptor’s hand – the sculptor was “mocking” the passions (with a play on the two meanings of the word “mocked” – “copied” them and “ridiculed” them); the “heart that fed them” is the heart of the ruthless tyrant himself, Ozymandias. The sense of the poem is that the arrogance of the ruler, his belief that his kingdom and his accomplishments would be unsurpassable and immortal, are ironically mocked by the fact that his statue, the only remnant of his reign, lies destroyed in “the lone and level sands,” and that human life, whether cruelly destructive or constructively creative, is temporal. The poem is also reflective of Shelley's own view of the transitory nature of his own poetry.