The spindle fibers disassemble during anaphase. As the spindle
fibers shorten during anaphase, they separate the chromatids from
one another and then move them to opposite poles.
The answer above stating that the Spindle Fibers disassemble
during anaphase is incorrect. If they were to disassemble at
anaphase it would completely halt the cell division process. The
spindle fibers disassemble during telophase.