The correct answer is "the tie that bound her to Spain has been severed". The "tie" refers to the colonial rule and "her" refers to America. To put in other words, Bolívar says in that sentence that the colonial rule of Spain over America is over.
With "kept the parts of that immense monarchy together", Bolívar is refering that only the concept of colonialism held the Spanish Empire together, but no one on the American continent felt bounded with the Spanish mainland.
The sentence "inspired in us is greater than the ocean between us" refers to the fact that America and Spain are so far from each other (there is literally an ocean between them), so there is little connection between the two. In this sentence he also says that the hate of the Spanish towards the Americans is bigger than the ocean between Spain and America.
