Explain how mutations & gene flow function antagonistically to each other...?

Question

...in terms of whether the DNA between two populations is the same or different.

Answer 1

When two populations are separated, each will accumulate its own mutations, unique from the other population.  If they are kept separated, eventually the accumulation of mutations can lead to reproductive isolation (i.e., speciation).  But, if the populations are not completely separated and there is some gene flow between them, then the mutations that arise in each population will be shared with the other, creating a homogenous gene pool.