Cell division is like making a photocopy of the entire blueprint of a completed building and then giving the copied blueprint to another contractor to build a completely new building.
Is this an accurate analogy of the process of cell division?
No. Cells do not copy all of their DNA (their blueprint) prior to cell division; only the DNA that codes for the cellular machinery and structure of that particular cell is copied.
Yes. Cells do replicate their DNA, and then an entire new cell is constructed using that newly copied DNA.
The analogy is only partially accurate. All of the DNA (the blueprint) is copied prior to cell division; however, an entire new cell is not constructed using this DNA, rather components of the original parent cell are divided equally between the two daughter cells.