How are different types of cells created from zygote?
I'm not sure about the first developmental stages but, given you already have hundreds of cells with slightly different physiology, the next developmental stages like dev. of neural tube happen through excretion of translation factors and growth factors in several cells. Each of those cells that are in a region where more than one excretion overlaps get a higher dose than the others. This is the signal for the cell to differentiate into another type, by changing its physiology. Such factor excretions are important events, and the genes encoding for the factors are evolutionally highly conserved (so called homeobox proteins).

However, this has nothing to do with mitosis. The newly divided cell does not decide on its own but reacts to a stimulus, like skin cells develop into skin cells because they are on the outside of the cell ball. Excreted factors do the fine tuning.