Final answer:
Microtubules are the cytoskeletal element that separates the cell's duplicated DNA molecules during eukaryotic cell division.
Step-by-step explanation:
The cytoskeletal element that separates the cell's duplicated DNA molecules during eukaryotic cell division is microtubules. Microtubules are bundles of tubulin proteins and are the structural elements of spindle fibers, which play a crucial role in chromosome separation during mitosis. They pull the replicated chromosomes to opposite ends of the dividing cell, ensuring each daughter cell receives a complete set of chromosomes.