Final answer:
The described stage is prophase, the first phase of mitosis, where the nuclear envelope dissolves, nucleoli disappear, centrosomes move, and the mitotic spindle forms.
Step-by-step explanation:
The stage of cell division described, characterized by the disappearance of the nuclear envelope, the disappearance of nucleoli, and the formation of the spindle in the cytoplasm, is known as prophase. During prophase, the nuclear envelope breaks down into small vesicles, and the nucleolus disperses. Centrosomes move to opposite poles of the cell and microtubules extend between them, forming the mitotic spindle. Sister chromatids start to coil more tightly and become visible under a microscope, marking the beginning stages of cell division.