Something that is almost always missed is the fact that we are ALL mutations. The term "species" is really just a way of grouping DNA that is sufficiently similar despite its differences. Sexual reproduction is a form of controlled mutation; it creates a new organism that at the DNA level is fundamentally different than either of its parents and which may exhibit particular abilities above and beyond either of its parents.
The human species has a vast number of genetic variations within its own genome. We don't look at these differences as "mutations", but that is in fact what these variations are. Over time, the basic characteristics of the human species have changed as we've moved into different environments with different selection pressures. The various overt physical differences among people alone is obvious evidence of this. Over time and space, these minor mutations add up and the differences become more pronounced. Every time you look at a fossil you ARE seeing a mutation, with different DNA and different characteristic tendencies than its ancestors. The problem is that it might take a linear sequence of hundreds of thousands of fossils before there was any really overt speciation, as the changes aren't really distinguishable (at least not from the fossil record) from one generation to the next. As it stands we don't have a linear sequence of hundreds of thousands of fossils, only a small number which are very spotty snapshots of the linear progression. So yes, the fossil record doesn't show clear mutation leading to speciation as hypothesized, but our current DNA and genome analytical capabilities have generally filled in the holes as to the mechanisms and such that the fossil record could not. Evolution was hypothesized LONG before DNA was discovered; many of the open questions in the evolutionary speciation hypothesis have been closed with recent technological and analytical developments in the DNA and genome related sciences.