Why does the DNA content of a cell get doubled in interphase? Why doesn't it become tripled or quadrupled? What's stopping it from doing so?
So in mitosis, the cell has to split itself into two cells; each daughter cell has a functional genome that may again split into more daughter cells. The cell replicates the DNA before dividing, so the error in replicating 3x or 4x is that upon division, the daughter cells will have more DNA than the initial cell, and every generation will have more DNA than the last. One replication ensures both daughter cells receive one functional genome. We can see the result of extra DNA in cases like Down Syndrome (trisomy of chromosome 21).
The cell controls this process by controlling the cyclins present in the cell temporally, namely cyclin-A and cyclin-E when we talk about DNA replication in S-phase,
Cyclin A resides in the nucleus during S phase where it is involved in the initiation and completion of DNA replication. As the cell passes from G1 into S phase, cyclin A associates with CDK2, replacing cyclin E. Cyclin E is responsible for initiating the assembly of the pre-replication complex. This complex makes chromatin capable of replication. When the amount of cyclin A/CDK2 complex reaches a threshold level, it terminates the assembly of the pre-replication complex made by cyclin E/CDK2. As the amount of Cyclin A/CDK2 complex increases, the complex initiates DNA replication.
Cyclin A has a second function in S phase, in addition to initiating DNA synthesis, Cyclin A ensures that DNA is replicated once per cell cycle by preventing the assembly of additional replication complexes. This is thought to occur through the phosphorylation of particular DNA replication machinery components, such as CDC6, by the cyclin A/CDK2 complex. Since the action of cyclin A/CDK2 inhibits that of cyclin E/CDK2, the sequential activation of cyclin E followed by the activation of cyclin A is important and tightly regulated in S phase.
Source: Cyclin A