Darwin didn't actually say we were mutating. All he did was to account for the origins of species that arrived on the Galapagos after they were created by volcanoes that rose from the sea floor. It was geologically recent, within the timeframe of, say an Ardipithecus, so all of those "mutations" happened right there. But why/how? And the rest is his theory of evolution.
Species can stabilize once they achieve evolutionary success. For the same reason you don't see rapid changes in humans that might be seen in fruit flies, all sorts of creatures are able to hang on. Cyanobacteria may have the same essential form they had billions of years ago. Some of the earliest of jawless fish are believed to still exist. Fossilized bugs, trapped in amber resemble bugs seen today.
Darwin never predicted any trends in change or stability. He merely explained how and why mutations will succeed at some point in time, and thus give rise to speciation.
The evolution of human intelligence adds a layer of complexity to the normal progress of natural selection. As long as humans can out-maneuver the kinds pressures that forced changes in our ancestral lines, we will tend to alter the odds of evolving into some future human, sub-human, or super-human species. Even the differences in traits we see by flying great distances, then stepping out into a terminal full of mostly brown or mostly blue eyes, for example, are subject to change, as people move around more and blend together. Something as simple as a long sleeved shirt can change the odds of all fair-skinned people becoming "extinct" in the tropics. But warnings against skin cancer - or just common sense - are all part of the bigger picture, something quite different than what Darwin was addressing.